Weierstrass Function (Fractal Cycles)THE WEIERSTRASS FUNCTION
f(x) = ∑(n=0)^∞ a^n * cos(b^n * π * x)
The Weierstrass Function is the sum of an infinite series of cosine functions, each with increasing frequency and decreasing amplitude. This creates powerful multi-scale oscillations within the range ⬍(-2;+2), resembling a system of self-repetitive patterns. You can zoom into any part of the output and observe similar proportions, mimicking the hidden order behind the irregularity and unpredictability of financial markets.
IT DOESN’T RELY ON ANY MARKET DATA, AS THE OUTPUT IS BASED PURELY ON A MATHEMATICAL FORMULA!
This script does not provide direct buy or sell signals and should be used as a tool for analyzing the market behavior through fractal geometry. The function is often used to model complex, chaotic systems, including natural phenomena and financial markets.
APPLICATIONS:
Timing Aspect: Identifies the phases of market cycles, helping to keep awareness of frequency of turning points
Price-Modeling features: The Amplitude, frequency, and scaling settings allow the indicator to simulate the trends and oscillations. Its nowhere-differentiable nature aligns with the market's inherent uncertainty. The fractured oscillations resemble sharp jumps, noise, and dips found in volatile markets.
SETTINGS
Amplitude Factor (a): Controls the size of each wave. A higher value makes the waves larger.
Frequency Factor (b): Determines how fast the waves oscillate. A higher value creates more frequent waves.
Ability to Invert the output: Just like any cosine function it starts its journey with a decline, which is not distinctive to the behavior of most assets. The default setting is in "inverted mode".
Scale Factor: Adjusts the speed at which the oscillations grow over time.
Number of Terms (n_terms): Increases the number of waves. More terms add complexity to the pattern.
Chaos
LPPL Critical Pulse (by BigBlueCheese) Version 1.1LPPL Critical Pulse (by BigBlueCheese)
I couldn’t locate a single script on TradingView that utilized the Log-Periodic Power Law (LPPL) and period doubling—key tools used by street professionals. Here is my first script…More to come.
Log-Periodic Power Law (LPPL)
LPPL is a mathematical framework used to model asset price bubbles that can help predict market crashes or corrections. It is based on the idea that speculative bubbles exhibit self-reinforcing, positive feedback behavior that leads to increasingly unsustainable price growth, followed by a crash or correction. But the big news is that because of the speculative behavior it can identify, it has equal application across many other instruments & timeframes.
The LPPL, has been around since the 1950’s and 1960’s where its theoretical foundation lies in the concepts of renormalized group theory and critical point behavior. Physicists Lev Landau, Vitaly Ginzburg & Kenneth Wilson contributed to how we can understand systems behave at critical points and was further developed by Benoit Mandelbrot via the concept of discrete scale invariance and log-periodicity. The concepts were popularized by Didier Sornette in Why Stock Markets Crash, where he used his model to detect when markets are experiencing extreme price movements, indicating the potential for a bubble to burst or a significant correction to occur. It is suspected that others like Jim Simons was an early adopter/adapter of this (and other) advanced mathematical concepts. LPPL is especially valuable for traders trying to anticipate rapid price movements—both upward and downward.
What is a Speculative Bubble?
A speculative bubble forms when an asset’s price skyrockets due to excitement from investors, pushing it well beyond its true value. At some point, this unsustainable growth leads to a crash, as the bubble “pops.” However, these crashes don’t need to be massive market-shaking events. They can also emerge from short-term price anomalies in any market or timeframe…..and they apply equally to upward & downward price moves. That is you can use this approach for both long and short trades.
Power Law & Log-Periodicity
The Power Law aspect describes how prices accelerate as they approach a critical point, forming a steep curve that signals instability.
The Log-Periodic component captures the oscillations that grow increasingly frequent as the price nears this tipping point, marking rising volatility.
Criticality in Trading: Feedback Loops, Attractors and Repellers
LPPL can be applied to financial markets by comparing them to natural systems prone to critical points, like avalanches or earthquakes. The key concept is criticality—the idea that, just like pressure building in an earthquake zone or snow stacking up on a mountain, there’s a feedback loop in markets where investor behavior becomes increasingly synchronized. This creates a self-reinforcing cycle, accelerating price movements until the system can no longer sustain the tension, and it collapses—similar to a critical phase shift in nature when physical systems experience sudden, catastrophic events when they reach a critical threshold.
In this context, the LPPL model aims to identify these critical points in financial markets by recognizing specific patterns in price movements, providing insight into the potential timing of major market shifts.
This is how markets can behave like attractors (drawing prices into unsustainable growth or collapses) or repellers (pushing them away through sudden corrections), depending on the balance of forces. LPPL captures this dynamic, helping traders anticipate when the market is nearing these critical moments.
Attractors are states or patterns that a system tends to gravitate towards over time, representing points of stability or equilibrium. Repellers are states that the system tends to avoid or move away from, representing instability or points of divergence.
In the context of the LPPL model, the market is seen as a dynamic system that is moving towards a critical point—often a bubble or a crash. The critical point itself can be viewed as an attractor, pulling the market toward a period of instability as prices accelerate and oscillations become more frequent. This movement reflects positive feedback loops, where investor behavior (e.g., herd mentality or speculative buying) reinforces the trend until it reaches an unsustainable level.
Conversely, once the critical point is reached, it can act as a repeller, causing the system (market) to rapidly move away from that state, often resulting in a crash or market correction. In essence, the LPPL model tries to identify these phases of movement toward or away from critical points, using attractors and repellers to describe the behavior of the system before and after major market events.
This dynamic interaction between stability and instability, or attractors and repellers, is a key feature of how Sornette’s LPPL approach models financial markets, emphasizing the market’s ability to oscillate between periods of calm and critical shifts.
Bubbles and Crashes in Any Timeframe
While people often think of bubbles and crashes as huge events like the Crash of 87, the Global Financial Crisis or COVID-19, they can also be much smaller or instrument specific. A short-term spike in a stock or a sudden currency drop can behave like a miniature bubble. LPPL helps spot these shorter-term price anomalies, making it versatile for traders looking for opportunities in all instruments and timeframes.
How Can I Use LPPL Critical Pulse?
Monitor price acceleration that signals unsustainable growth/movement .
Spot volatility, oscillations, extensions and compressions and exhaustion as the market nears critical instability and levels.
Combine with other indicators to help time entries and exits, manage risk as markets approach/consolidate/leave critical levels.
LPPL Critical Pulse (LPPLCP)
LPPLCP is based on LPPL principles that identify potential upward and downward market movements, exhaustion and consolidation periods.
Visualization
The LPPL line is smoothed using a moving average to reduce noise, and the result is scaled to fit within the price range of the past 100 bars, aligning the LPPL line with the price movements on the chart.
Dynamic LPPL Line Plot:
A smoothed and scaled LPPL line plotted directly on the price chart.
• Color-Coded Trend Analysis: The LPPL line changes color dynamically based on the conditions of slope and acceleration to reflect market behaviors such as period doubling or exhaustion.
1. White (Exhaustion/Consolidation Condition): Indicates that both the slope and the acceleration of the LPPL line are zero, suggesting a potential market flattening or exhaustion/consolidation. At the end of this period, a new trend may emerge OR the prior trend may reassert itself.
2. Purple (Period Doubling): This color appears when the LPPL model detects rapid changes in acceleration, indicating the potential for a market turning point (period doubling). The slope of the LPPL line during this period suggests whether the market is moving upward or downward.
3. Green (Positive Slope with Increasing Acceleration): A green LPPL line suggests that the market is in an upward trend, with increasing acceleration.
4. Red (Negative Slope with Decreasing Acceleration): A red LPPL line indicates a downward market trend with decreasing acceleration.
5. Yellow (Neutral): Yellow is the default color when none of the specific conditions (exhaustion, period doubling, positive/negative slope with acceleration) are met, i.e. generally a continuation of the prior condition but at a slower pace.
Customization for Any Market
LPPL Critical Pulse has application across most time frames for pretty much whatever you want to trade…stocks, commodities, currencies, futures, and more. You will have to tweak the inputs to optimize for the market(s) you choose to trade.
Inputs
1. Lookback Period for Adaptation
o Type: Integer
o Default: 1
o Description: Defines the lookback period for calculating the Simple Moving Average (SMA) and Standard Deviation (StDev) used in the LPPL model. A higher value smooths the calculations over a longer period.
2. Period Doubling Threshold
o Type: Float
o Default: 0.01
o Description: Determines the sensitivity for detecting period doubling in the LPPL line. A lower threshold increases sensitivity.
3. Flattening Threshold
o Type: Float
o Default: 0.01
o Description: This input is not actively used in the current version but can be modified for further customizations in the LPPL model.
4. Period Doubling Acceleration Threshold
o Type: Float
o Default: 0.02
o Description: This controls the threshold for detecting rapid changes in the LPPL acceleration, helping identify when period doubling occurs.
Calculation Components
The LPPL line is calculated using several components:
• SMA (A): The simple moving average of the closing prices over the selected lookback period.
• Standard Deviation (B, C): These parameters are calculated based on the standard deviation of prices and control the amplitude of the LPPL oscillations.
• Exponential Decay: The LPPL line decays as it approaches a theoretical critical time (tc), where market crashes or rapid changes may occur.
Disclaimer.
Not investment advice. Use at your own risk. Past results do not represent and are not indicative of future results
GKD-C Chaos Visual Averages [Loxx]The Giga Kaleidoscope GKD-C Chaos Visual Averages is a confirmation module included in Loxx's "Giga Kaleidoscope Modularized Trading System."
? GKD-C Chaos Visual Averages
One of the most common errors made by inexperienced traders is attempting to extract excessive information from a single chart by employing numerous unnecessary indicators. The outcome often entails a cluttered chart filled with lines, erratic patterns, and an assortment of distracting elements, all of which weave a conflicting narrative for the trader.
This on-screen "clutter" can bewilder new traders, compelling them to open or maintain unprofitable positions until the dreaded Margin Call looms.
The advice is clear: Keep it simple. But how can one achieve this simplicity?
Enter the Chaos Visual Averages indicator
This indicator not only generates the most precise reversal signals available but also equips traders to seamlessly align with prevailing trends and engage in counter-trend trading to realign with the overall market direction.
For traders opting to employ Chaos, a clean and uncluttered chart is recommended, eschewing the use of additional oscillators, as all the necessary components are already integrated into Visual Chaos.
Tip: Crafting a straightforward and profitable trading system with Chaos involves marking Weekly and Daily Support and Resistance lines and executing counter-trend trades as price approaches these key levels, utilizing the Overbought Extreme and Oversold Extreme signals from the 15-minute Chaos.
Pros:
Remarkable precision in identifying market reversals.
Visually appealing and easily interpretable market conditions.
Suitable for both trend-following and counter-trend trading.
Robust back-testing results (nearly 95% accuracy on "Extreme" signals).
An all-encompassing indicator capable of supporting a livelihood through trading.
Cons:
In rare instances, even with Overbought "Extreme" and Oversold "Extreme" conditions, the indicator may lead to trading against a robust trend, resulting in significant drawdowns before eventual price reversal.
Overbought "Extreme" and Oversold "Extreme" signals can be infrequent when trading on the 15-minute timeframe and above. To mitigate this, it is advisable to trade at least 8 major currency pairs to receive "Extreme" signals with greater frequency."
? Giga Kaleidoscope Modularized Trading System
Core components of an NNFX algorithmic trading strategy
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:
1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted
8. Metamorphosis - a technical indicator that produces a compound signal from the combination of other GKD indicators*
*(not part of the NNFX algorithm)
What is Volatility in the NNFX trading system?
In the NNFX (No Nonsense Forex) trading system, ATR (Average True Range) is typically used to measure the volatility of an asset. It is used as a part of the system to help determine the appropriate stop loss and take profit levels for a trade. ATR is calculated by taking the average of the true range values over a specified period.
True range is calculated as the maximum of the following values:
-Current high minus the current low
-Absolute value of the current high minus the previous close
-Absolute value of the current low minus the previous close
ATR is a dynamic indicator that changes with changes in volatility. As volatility increases, the value of ATR increases, and as volatility decreases, the value of ATR decreases. By using ATR in NNFX system, traders can adjust their stop loss and take profit levels according to the volatility of the asset being traded. This helps to ensure that the trade is given enough room to move, while also minimizing potential losses.
Other types of volatility include True Range Double (TRD), Close-to-Close, and Garman-Klass
What is a Baseline indicator?
The baseline is essentially a moving average, and is used to determine the overall direction of the market.
The baseline in the NNFX system is used to filter out trades that are not in line with the long-term trend of the market. The baseline is plotted on the chart along with other indicators, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR).
Trades are only taken when the price is in the same direction as the baseline. For example, if the baseline is sloping upwards, only long trades are taken, and if the baseline is sloping downwards, only short trades are taken. This approach helps to ensure that trades are in line with the overall trend of the market, and reduces the risk of entering trades that are likely to fail.
By using a baseline in the NNFX system, traders can have a clear reference point for determining the overall trend of the market, and can make more informed trading decisions. The baseline helps to filter out noise and false signals, and ensures that trades are taken in the direction of the long-term trend.
What is a Confirmation indicator?
Confirmation indicators are technical indicators that are used to confirm the signals generated by primary indicators. Primary indicators are the core indicators used in the NNFX system, such as the Average True Range (ATR), the Moving Average (MA), and the Relative Strength Index (RSI).
The purpose of the confirmation indicators is to reduce false signals and improve the accuracy of the trading system. They are designed to confirm the signals generated by the primary indicators by providing additional information about the strength and direction of the trend.
Some examples of confirmation indicators that may be used in the NNFX system include the Bollinger Bands, the MACD (Moving Average Convergence Divergence), and the MACD Oscillator. These indicators can provide information about the volatility, momentum, and trend strength of the market, and can be used to confirm the signals generated by the primary indicators.
In the NNFX system, confirmation indicators are used in combination with primary indicators and other filters to create a trading system that is robust and reliable. By using multiple indicators to confirm trading signals, the system aims to reduce the risk of false signals and improve the overall profitability of the trades.
What is a Continuation indicator?
In the NNFX (No Nonsense Forex) trading system, a continuation indicator is a technical indicator that is used to confirm a current trend and predict that the trend is likely to continue in the same direction. A continuation indicator is typically used in conjunction with other indicators in the system, such as a baseline indicator, to provide a comprehensive trading strategy.
What is a Volatility/Volume indicator?
Volume indicators, such as the On Balance Volume (OBV), the Chaikin Money Flow (CMF), or the Volume Price Trend (VPT), are used to measure the amount of buying and selling activity in a market. They are based on the trading volume of the market, and can provide information about the strength of the trend. In the NNFX system, volume indicators are used to confirm trading signals generated by the Moving Average and the Relative Strength Index. Volatility indicators include Average Direction Index, Waddah Attar, and Volatility Ratio. In the NNFX trading system, volatility is a proxy for volume and vice versa.
By using volume indicators as confirmation tools, the NNFX trading system aims to reduce the risk of false signals and improve the overall profitability of trades. These indicators can provide additional information about the market that is not captured by the primary indicators, and can help traders to make more informed trading decisions. In addition, volume indicators can be used to identify potential changes in market trends and to confirm the strength of price movements.
What is an Exit indicator?
The exit indicator is used in conjunction with other indicators in the system, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR), to provide a comprehensive trading strategy.
The exit indicator in the NNFX system can be any technical indicator that is deemed effective at identifying optimal exit points. Examples of exit indicators that are commonly used include the Parabolic SAR, the Average Directional Index (ADX), and the Chandelier Exit.
The purpose of the exit indicator is to identify when a trend is likely to reverse or when the market conditions have changed, signaling the need to exit a trade. By using an exit indicator, traders can manage their risk and prevent significant losses.
In the NNFX system, the exit indicator is used in conjunction with a stop loss and a take profit order to maximize profits and minimize losses. The stop loss order is used to limit the amount of loss that can be incurred if the trade goes against the trader, while the take profit order is used to lock in profits when the trade is moving in the trader's favor.
Overall, the use of an exit indicator in the NNFX trading system is an important component of a comprehensive trading strategy. It allows traders to manage their risk effectively and improve the profitability of their trades by exiting at the right time.
What is an Metamorphosis indicator?
The concept of a metamorphosis indicator involves the integration of two or more GKD indicators to generate a compound signal. This is achieved by evaluating the accuracy of each indicator and selecting the signal from the indicator with the highest accuracy. As an illustration, let's consider a scenario where we calculate the accuracy of 10 indicators and choose the signal from the indicator that demonstrates the highest accuracy.
The resulting output from the metamorphosis indicator can then be utilized in a GKD-BT backtest by occupying a slot that aligns with the purpose of the metamorphosis indicator. The slot can be a GKD-B, GKD-C, or GKD-E slot, depending on the specific requirements and objectives of the indicator. This allows for seamless integration and utilization of the compound signal within the GKD-BT framework.
How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v2.0 system has five types of modules (indicators/strategies). These modules are:
1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)
6. GKD-M - Metamorphosis module (Metamorphosis, Number 8 in the NNFX algorithm, but not part of the NNFX algorithm)
(additional module types will added in future releases)
Each module interacts with every module by passing data to A backtest module wherein the various components of the GKD system are combined to create a trading signal.
That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.
This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.
What does the application of the GKD trading system look like?
Example trading system:
Backtest: Multi-Ticker CC Backtest
Baseline: Hull Moving Average
Volatility/Volume: Hurst Exponent
Confirmation 1: Advance Trend Pressure as shown on the chart above
Confirmation 2: uf2018
Continuation: Coppock Curve
Exit: Rex Oscillator
Metamorphosis: Baseline Optimizer
Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, GKD-M, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD system.
? Giga Kaleidoscope Modularized Trading System Signals
Standard Entry
1. GKD-C Confirmation gives signal
2. Baseline agrees
3. Price inside Goldie Locks Zone Minimum
4. Price inside Goldie Locks Zone Maximum
5. Confirmation 2 agrees
6. Volatility/Volume agrees
1-Candle Standard Entry
1a. GKD-C Confirmation gives signal
2a. Baseline agrees
3a. Price inside Goldie Locks Zone Minimum
4a. Price inside Goldie Locks Zone Maximum
Next Candle
1b. Price retraced
2b. Baseline agrees
3b. Confirmation 1 agrees
4b. Confirmation 2 agrees
5b. Volatility/Volume agrees
Baseline Entry
1. GKD-B Baseline gives signal
2. Confirmation 1 agrees
3. Price inside Goldie Locks Zone Minimum
4. Price inside Goldie Locks Zone Maximum
5. Confirmation 2 agrees
6. Volatility/Volume agrees
7. Confirmation 1 signal was less than 'Maximum Allowable PSBC Bars Back' prior
1-Candle Baseline Entry
1a. GKD-B Baseline gives signal
2a. Confirmation 1 agrees
3a. Price inside Goldie Locks Zone Minimum
4a. Price inside Goldie Locks Zone Maximum
5a. Confirmation 1 signal was less than 'Maximum Allowable PSBC Bars Back' prior
Next Candle
1b. Price retraced
2b. Baseline agrees
3b. Confirmation 1 agrees
4b. Confirmation 2 agrees
5b. Volatility/Volume agrees
Volatility/Volume Entry
1. GKD-V Volatility/Volume gives signal
2. Confirmation 1 agrees
3. Price inside Goldie Locks Zone Minimum
4. Price inside Goldie Locks Zone Maximum
5. Confirmation 2 agrees
6. Baseline agrees
7. Confirmation 1 signal was less than 7 candles prior
1-Candle Volatility/Volume Entry
1a. GKD-V Volatility/Volume gives signal
2a. Confirmation 1 agrees
3a. Price inside Goldie Locks Zone Minimum
4a. Price inside Goldie Locks Zone Maximum
5a. Confirmation 1 signal was less than 'Maximum Allowable PSVVC Bars Back' prior
Next Candle
1b. Price retraced
2b. Volatility/Volume agrees
3b. Confirmation 1 agrees
4b. Confirmation 2 agrees
5b. Baseline agrees
Confirmation 2 Entry
1. GKD-C Confirmation 2 gives signal
2. Confirmation 1 agrees
3. Price inside Goldie Locks Zone Minimum
4. Price inside Goldie Locks Zone Maximum
5. Volatility/Volume agrees
6. Baseline agrees
7. Confirmation 1 signal was less than 7 candles prior
1-Candle Confirmation 2 Entry
1a. GKD-C Confirmation 2 gives signal
2a. Confirmation 1 agrees
3a. Price inside Goldie Locks Zone Minimum
4a. Price inside Goldie Locks Zone Maximum
5a. Confirmation 1 signal was less than 'Maximum Allowable PSC2C Bars Back' prior
Next Candle
1b. Price retraced
2b. Confirmation 2 agrees
3b. Confirmation 1 agrees
4b. Volatility/Volume agrees
5b. Baseline agrees
PullBack Entry
1a. GKD-B Baseline gives signal
2a. Confirmation 1 agrees
3a. Price is beyond 1.0x Volatility of Baseline
Next Candle
1b. Price inside Goldie Locks Zone Minimum
2b. Price inside Goldie Locks Zone Maximum
3b. Confirmation 1 agrees
4b. Confirmation 2 agrees
5b. Volatility/Volume agrees
Continuation Entry
1. Standard Entry, 1-Candle Standard Entry, Baseline Entry, 1-Candle Baseline Entry, Volatility/Volume Entry, 1-Candle Volatility/Volume Entry, Confirmation 2 Entry, 1-Candle Confirmation 2 Entry, or Pullback entry triggered previously
2. Baseline hasn't crossed since entry signal trigger
4. Confirmation 1 agrees
5. Baseline agrees
6. Confirmation 2 agrees
WIPFunctionLyaponovLibrary "WIPFunctionLyaponov"
Lyapunov exponents are mathematical measures used to describe the behavior of a system over
time. They are named after Russian mathematician Alexei Lyapunov, who first introduced the concept in the
late 19th century. The exponent is defined as the rate at which a particular function or variable changes
over time, and can be positive, negative, or zero.
Positive exponents indicate that a system tends to grow or expand over time, while negative exponents
indicate that a system tends to shrink or decay. Zero exponents indicate that the system does not change
significantly over time. Lyapunov exponents are used in various fields of science and engineering, including
physics, economics, and biology, to study the long-term behavior of complex systems.
~ generated description from vicuna13b
---
To calculate the Lyapunov Exponent (LE) of a given Time Series, we need to follow these steps:
1. Firstly, you should have access to your data in some format like CSV or Excel file. If not, then you can collect it manually using tools such as stopwatches and measuring tapes.
2. Once the data is collected, clean it up by removing any outliers that may skew results. This step involves checking for inconsistencies within your dataset (e.g., extremely large or small values) and either discarding them entirely or replacing with more reasonable estimates based on surrounding values.
3. Next, you need to determine the dimension of your time series data. In most cases, this will be equal to the number of variables being measured in each observation period (e.g., temperature, humidity, wind speed).
4. Now that we have a clean dataset with known dimensions, we can calculate the LE for our Time Series using the following formula:
λ = log(||M^T * M - I||)/log(||v||)
where:
λ (Lyapunov Exponent) is the quantity that will be calculated.
||...|| denotes an Euclidean norm of a vector or matrix, which essentially means taking the square root of the sum of squares for each element in the vector/matrix.
M represents our Jacobian Matrix whose elements are given by:
J_ij = (∂fj / ∂xj) where fj is the jth variable and xj is the ith component of the initial condition vector x(t). In other words, each element in this matrix represents how much a small change in one variable affects another.
I denotes an identity matrix whose elements are all equal to 1 (or any constant value if you prefer). This term essentially acts as a baseline for comparison purposes since we want our Jacobian Matrix M^T * M to be close to it when the system is stable and far away from it when the system is unstable.
v represents an arbitrary vector whose Euclidean norm ||v|| will serve as a scaling factor in our calculation. The choice of this particular vector does not matter since we are only interested in its magnitude (i.e., length) for purposes of normalization. However, if you want to ensure that your results are accurate and consistent across different datasets or scenarios, it is recommended to use the same initial condition vector x(t) as used earlier when calculating our Jacobian Matrix M.
5. Finally, once we have calculated λ using the formula above, we can interpret its value in terms of stability/instability for our Time Series data:
- If λ < 0, then this indicates that the system is stable (i.e., nearby trajectories will converge towards each other over time).
- On the other hand, if λ > 0, then this implies that the system is unstable (i.e., nearby trajectories will diverge away from one another over time).
~ generated description from airoboros33b
---
Reference:
en.wikipedia.org
www.collimator.ai
blog.abhranil.net
www.researchgate.net
physics.stackexchange.com
---
This is a work in progress, it may contain errors so use with caution.
If you find flaws or suggest something new, please leave a comment bellow.
_measure_function(i)
helper function to get the name of distance function by a index (0 -> 13).\
Functions: SSD, Euclidean, Manhattan, Minkowski, Chebyshev, Correlation, Cosine, Camberra, MAE, MSE, Lorentzian, Intersection, Penrose Shape, Meehl.
Parameters:
i (int)
_test(L)
Helper function to test the output exponents state system and outputs description into a string.
Parameters:
L (float )
estimate(X, initial_distance, distance_function)
Estimate the Lyaponov Exponents for multiple series in a row matrix.
Parameters:
X (map)
initial_distance (float) : Initial distance limit.
distance_function (string) : Name of the distance function to be used, default:`ssd`.
Returns: List of Lyaponov exponents.
max(L)
Maximal Lyaponov Exponent.
Parameters:
L (float ) : List of Lyapunov exponents.
Returns: Highest exponent.
GKD-V Cercos Chaos vs Movement [Loxx]Giga Kaleidoscope GKD-V Cercos Chaos vs Movement is a Volatility/Volume module included in Loxx's "Giga Kaleidoscope Modularized Trading System".
█ GKD-V Cercos Chaos vs Movement
The following aims to provide a detailed explanation of Cercos Chaos vs Movement that helps traders determine market volatility by comparing two different measures: Buffer Move and Buffer Chaos. This indicator is non-directional and should be paired with a directional indicator to provide trading signals.
The first step in the process is defining a custom function that implements a variant of the sigmoid function. This function has a parameter that allows the output to be limited to the range of if desired. The sigmoid function will later be used to normalize the Buffer Chaos value.
Next, several input parameters are introduced, which can be adjusted by the user. These parameters include the period, chaos strength, chaos width, and movement strength. These values are essential to customizing the behavior of the indicator and adapting it to different market conditions and trading styles.
The wicks of the candles in the given time series are then calculated by subtracting the absolute difference between the open and close prices from the difference between the high and low prices. This step is crucial in determining the level of volatility in the market.
Subsequently, the highest high and lowest low over the defined period are identified by examining the maximum and minimum values of the open and close prices. This information is essential for calculating the total movement in the market over the period being analyzed.
Once the highest high and lowest low are found, the Buffer Move and Buffer Chaos values are calculated. The Buffer Move is the sum of the differences between the high and low prices for each candle in the period. This measure helps to identify the overall price movement in the market during the period.
On the other hand, the Buffer Chaos represents the sum of the wicks' lengths for each candle in the period. This measure is used to identify the level of uncertainty and disorder in the market during the period.
In the next step, the total movement in the market is calculated by subtracting the lowest low from the highest high. This value is then used to normalize the Buffer Move and Buffer Chaos values, ensuring they are on a comparable scale.
A comparison is made between the normalized Buffer Move and Buffer Chaos values. If the Buffer Move value is greater than the Buffer Chaos value, it indicates that there is enough volatility in the market to trade long or short. In such a case, the indicator suggests that the market conditions are favorable for trading. However, as this indicator is non-directional, a directional indicator should be used in conjunction with it to provide trading signals.
In conclusion, this custom trading indicator provides valuable insights into market volatility by comparing the Buffer Move and Buffer Chaos values. By offering a non-directional perspective, traders can use this indicator to gauge the potential for profitable trades and make informed decisions by pairing it with a directional indicator.
Additional Features
This indicator allows you to select from 33 source types. They are as follows:
Close
Open
High
Low
Median
Typical
Weighted
Average
Average Median Body
Trend Biased
Trend Biased (Extreme)
HA Close
HA Open
HA High
HA Low
HA Median
HA Typical
HA Weighted
HA Average
HA Average Median Body
HA Trend Biased
HA Trend Biased (Extreme)
HAB Close
HAB Open
HAB High
HAB Low
HAB Median
HAB Typical
HAB Weighted
HAB Average
HAB Average Median Body
HAB Trend Biased
HAB Trend Biased (Extreme)
What are Heiken Ashi "better" candles?
Heiken Ashi "better" candles are a modified version of the standard Heiken Ashi candles, which are a popular charting technique used in technical analysis. Heiken Ashi candles help traders identify trends and potential reversal points by smoothing out price data and reducing market noise. The "better formula" was proposed by Sebastian Schmidt in an article published by BNP Paribas in Warrants & Zertifikate, a German magazine, in August 2004. The aim of this formula is to further improve the smoothing of the Heiken Ashi chart and enhance its effectiveness in identifying trends and reversals.
Standard Heiken Ashi candles are calculated using the following formulas:
Heiken Ashi Close = (Open + High + Low + Close) / 4
Heiken Ashi Open = (Previous Heiken Ashi Open + Previous Heiken Ashi Close) / 2
Heiken Ashi High = Max (High, Heiken Ashi Open, Heiken Ashi Close)
Heiken Ashi Low = Min (Low, Heiken Ashi Open, Heiken Ashi Close)
The "better formula" modifies the standard Heiken Ashi calculation by incorporating additional smoothing, which can help reduce noise and make it easier to identify trends and reversals. The modified formulas for Heiken Ashi "better" candles are as follows:
Better Heiken Ashi Close = (Open + High + Low + Close) / 4
Better Heiken Ashi Open = (Previous Better Heiken Ashi Open + Previous Better Heiken Ashi Close) / 2
Better Heiken Ashi High = Max (High, Better Heiken Ashi Open, Better Heiken Ashi Close)
Better Heiken Ashi Low = Min (Low, Better Heiken Ashi Open, Better Heiken Ashi Close)
Smoothing Factor = 2 / (N + 1), where N is the chosen period for smoothing
Smoothed Better Heiken Ashi Open = (Better Heiken Ashi Open * Smoothing Factor) + (Previous Smoothed Better Heiken Ashi Open * (1 - Smoothing Factor))
Smoothed Better Heiken Ashi Close = (Better Heiken Ashi Close * Smoothing Factor) + (Previous Smoothed Better Heiken Ashi Close * (1 - Smoothing Factor))
The smoothed Better Heiken Ashi Open and Close values are then used to calculate the smoothed Better Heiken Ashi High and Low values, resulting in "better" candles that provide a clearer representation of the market trend and potential reversal points.
It's important to note that, like any other technical analysis tool, Heiken Ashi "better" candles are not foolproof and should be used in conjunction with other indicators and analysis techniques to make well-informed trading decisions.
Heiken Ashi "better" candles, as mentioned previously, provide a clearer representation of market trends and potential reversal points by reducing noise and smoothing out price data. When using these candles in conjunction with other technical analysis tools and indicators, traders can gain valuable insights into market behavior and make more informed decisions.
To effectively use Heiken Ashi "better" candles in your trading strategy, consider the following tips:
Trend Identification: Heiken Ashi "better" candles can help you identify the prevailing trend in the market. When the majority of the candles are green (or another color, depending on your chart settings) and there are no or few lower wicks, it may indicate a strong uptrend. Conversely, when the majority of the candles are red (or another color) and there are no or few upper wicks, it may signal a strong downtrend.
Trend Reversals: Look for potential trend reversals when a change in the color of the candles occurs, especially when accompanied by longer wicks. For example, if a green candle with a long lower wick is followed by a red candle, it could indicate a bearish reversal. Similarly, a red candle with a long upper wick followed by a green candle may suggest a bullish reversal.
Support and Resistance: You can use Heiken Ashi "better" candles to identify potential support and resistance levels. When the candles are consistently moving in one direction and then suddenly change color with longer wicks, it could indicate the presence of a support or resistance level.
Stop-Loss and Take-Profit: Using Heiken Ashi "better" candles can help you manage risk by determining optimal stop-loss and take-profit levels. For instance, you can place your stop-loss below the low of the most recent green candle in an uptrend or above the high of the most recent red candle in a downtrend.
Confirming Signals: Heiken Ashi "better" candles should be used in conjunction with other technical indicators, such as moving averages, oscillators, or chart patterns, to confirm signals and improve the accuracy of your analysis.
In this implementation, you have the choice of AMA, KAMA, or T3 smoothing. These are as follows:
Kaufman Adaptive Moving Average (KAMA)
The Kaufman Adaptive Moving Average (KAMA) is a type of adaptive moving average used in technical analysis to smooth out price fluctuations and identify trends. The KAMA adjusts its smoothing factor based on the market's volatility, making it more responsive in volatile markets and smoother in calm markets. The KAMA is calculated using three different efficiency ratios that determine the appropriate smoothing factor for the current market conditions. These ratios are based on the noise level of the market, the speed at which the market is moving, and the length of the moving average. The KAMA is a popular choice among traders who prefer to use adaptive indicators to identify trends and potential reversals.
Adaptive Moving Average
The Adaptive Moving Average (AMA) is a type of moving average that adjusts its sensitivity to price movements based on market conditions. It uses a ratio between the current price and the highest and lowest prices over a certain lookback period to determine its level of smoothing. The AMA can help reduce lag and increase responsiveness to changes in trend direction, making it useful for traders who want to follow trends while avoiding false signals. The AMA is calculated by multiplying a smoothing constant with the difference between the current price and the previous AMA value, then adding the result to the previous AMA value.
T3
The T3 moving average is a type of technical indicator used in financial analysis to identify trends in price movements. It is similar to the Exponential Moving Average (EMA) and the Double Exponential Moving Average (DEMA), but uses a different smoothing algorithm.
The T3 moving average is calculated using a series of exponential moving averages that are designed to filter out noise and smooth the data. The resulting smoothed data is then weighted with a non-linear function to produce a final output that is more responsive to changes in trend direction.
The T3 moving average can be customized by adjusting the length of the moving average, as well as the weighting function used to smooth the data. It is commonly used in conjunction with other technical indicators as part of a larger trading strategy.
█ Giga Kaleidoscope Modularized Trading System
Core components of an NNFX algorithmic trading strategy
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:
1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted
What is Volatility in the NNFX trading system?
In the NNFX (No Nonsense Forex) trading system, ATR (Average True Range) is typically used to measure the volatility of an asset. It is used as a part of the system to help determine the appropriate stop loss and take profit levels for a trade. ATR is calculated by taking the average of the true range values over a specified period.
True range is calculated as the maximum of the following values:
-Current high minus the current low
-Absolute value of the current high minus the previous close
-Absolute value of the current low minus the previous close
ATR is a dynamic indicator that changes with changes in volatility. As volatility increases, the value of ATR increases, and as volatility decreases, the value of ATR decreases. By using ATR in NNFX system, traders can adjust their stop loss and take profit levels according to the volatility of the asset being traded. This helps to ensure that the trade is given enough room to move, while also minimizing potential losses.
Other types of volatility include True Range Double (TRD), Close-to-Close, and Garman-Klass
What is a Baseline indicator?
The baseline is essentially a moving average, and is used to determine the overall direction of the market.
The baseline in the NNFX system is used to filter out trades that are not in line with the long-term trend of the market. The baseline is plotted on the chart along with other indicators, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR).
Trades are only taken when the price is in the same direction as the baseline. For example, if the baseline is sloping upwards, only long trades are taken, and if the baseline is sloping downwards, only short trades are taken. This approach helps to ensure that trades are in line with the overall trend of the market, and reduces the risk of entering trades that are likely to fail.
By using a baseline in the NNFX system, traders can have a clear reference point for determining the overall trend of the market, and can make more informed trading decisions. The baseline helps to filter out noise and false signals, and ensures that trades are taken in the direction of the long-term trend.
What is a Confirmation indicator?
Confirmation indicators are technical indicators that are used to confirm the signals generated by primary indicators. Primary indicators are the core indicators used in the NNFX system, such as the Average True Range (ATR), the Moving Average (MA), and the Relative Strength Index (RSI).
The purpose of the confirmation indicators is to reduce false signals and improve the accuracy of the trading system. They are designed to confirm the signals generated by the primary indicators by providing additional information about the strength and direction of the trend.
Some examples of confirmation indicators that may be used in the NNFX system include the Bollinger Bands, the MACD (Moving Average Convergence Divergence), and the MACD Oscillator. These indicators can provide information about the volatility, momentum, and trend strength of the market, and can be used to confirm the signals generated by the primary indicators.
In the NNFX system, confirmation indicators are used in combination with primary indicators and other filters to create a trading system that is robust and reliable. By using multiple indicators to confirm trading signals, the system aims to reduce the risk of false signals and improve the overall profitability of the trades.
What is a Continuation indicator?
In the NNFX (No Nonsense Forex) trading system, a continuation indicator is a technical indicator that is used to confirm a current trend and predict that the trend is likely to continue in the same direction. A continuation indicator is typically used in conjunction with other indicators in the system, such as a baseline indicator, to provide a comprehensive trading strategy.
What is a Volatility/Volume indicator?
Volume indicators, such as the On Balance Volume (OBV), the Chaikin Money Flow (CMF), or the Volume Price Trend (VPT), are used to measure the amount of buying and selling activity in a market. They are based on the trading volume of the market, and can provide information about the strength of the trend. In the NNFX system, volume indicators are used to confirm trading signals generated by the Moving Average and the Relative Strength Index. Volatility indicators include Average Direction Index, Waddah Attar, and Volatility Ratio. In the NNFX trading system, volatility is a proxy for volume and vice versa.
By using volume indicators as confirmation tools, the NNFX trading system aims to reduce the risk of false signals and improve the overall profitability of trades. These indicators can provide additional information about the market that is not captured by the primary indicators, and can help traders to make more informed trading decisions. In addition, volume indicators can be used to identify potential changes in market trends and to confirm the strength of price movements.
What is an Exit indicator?
The exit indicator is used in conjunction with other indicators in the system, such as the Moving Average (MA), the Relative Strength Index (RSI), and the Average True Range (ATR), to provide a comprehensive trading strategy.
The exit indicator in the NNFX system can be any technical indicator that is deemed effective at identifying optimal exit points. Examples of exit indicators that are commonly used include the Parabolic SAR, the Average Directional Index (ADX), and the Chandelier Exit.
The purpose of the exit indicator is to identify when a trend is likely to reverse or when the market conditions have changed, signaling the need to exit a trade. By using an exit indicator, traders can manage their risk and prevent significant losses.
In the NNFX system, the exit indicator is used in conjunction with a stop loss and a take profit order to maximize profits and minimize losses. The stop loss order is used to limit the amount of loss that can be incurred if the trade goes against the trader, while the take profit order is used to lock in profits when the trade is moving in the trader's favor.
Overall, the use of an exit indicator in the NNFX trading system is an important component of a comprehensive trading strategy. It allows traders to manage their risk effectively and improve the profitability of their trades by exiting at the right time.
How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v1.0 system has five types of modules (indicators/strategies). These modules are:
1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)
(additional module types will added in future releases)
Each module interacts with every module by passing data between modules. Data is passed between each module as described below:
GKD-B => GKD-V => GKD-C(1) => GKD-C(2) => GKD-C(Continuation) => GKD-E => GKD-BT
That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.
This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.
What does the application of the GKD trading system look like?
Example trading system:
Backtest: Strategy with 1-3 take profits, trailing stop loss, multiple types of PnL volatility, and 2 backtesting styles
Baseline: Hull Moving Average
Volatility/Volume: Cercos Chaos vs Movement as shown on the chart above
Confirmation 1: Fisher Transform
Confirmation 2: Williams Percent Range
Continuation: Cercos Chaos vs Movement
Exit: Rex Oscillator
Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD protocol chain.
Giga Kaleidoscope Modularized Trading System Signals (based on the NNFX algorithm)
Standard Entry
1. GKD-C Confirmation 1 Signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior
Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior
Continuation Entry
1. Standard Entry, Baseline Entry, or Pullback; entry triggered previously
2. GKD-B Baseline hasn't crossed since entry signal trigger
3. GKD-C Confirmation Continuation Indicator signals
4. GKD-C Confirmation 1 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 2 agrees
1-Candle Rule Standard Entry
1. GKD-C Confirmation 1 signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
1-Candle Rule Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees
1-Candle Rule Volatility/Volume Entry
1. GKD-V Volatility/Volume signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close)
2. GKD-B Volatility/Volume agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-B Baseline agrees
PullBack Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is beyond 1.0x Volatility of Baseline
Next Candle:
1. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
2. GKD-C Confirmation 1 agrees
3. GKD-C Confirmation 2 agrees
4. GKD-V Volatility/Volume Agrees
]█ Setting up the GKD
The GKD system involves chaining indicators together. These are the steps to set this up.
Use a GKD-C indicator alone on a chart
1. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Simple"
Use a GKD-V indicator alone on a chart
**nothing, it's already useable on the chart without any settings changes
Use a GKD-B indicator alone on a chart
**nothing, it's already useable on the chart without any settings changes
Baseline (Baseline, Backtest)
1. Import the GKD-B Baseline into the GKD-BT Backtest: "Input into Volatility/Volume or Backtest (Baseline testing)"
2. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Baseline"
Volatility/Volume (Volatility/Volume, Backte st)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Solo"
2. Inside the GKD-V indicator, change the "Signal Type" setting to "Crossing" (neither traditional nor both can be backtested)
3. Import the GKD-V indicator into the GKD-BT Backtest: "Input into C1 or Backtest"
4. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Volatility/Volume"
5. Inside the GKD-BT Backtest, a) change the setting "Backtest Type" to "Trading" if using a directional GKD-V indicator; or, b) change the setting "Backtest Type" to "Full" if using a directional or non-directional GKD-V indicator (non-directional GKD-V can only test Longs and Shorts separately)
6. If "Backtest Type" is set to "Full": Inside the GKD-BT Backtest, change the setting "Backtest Side" to "Long" or "Short
7. If "Backtest Type" is set to "Full": To allow the system to open multiple orders at one time so you test all Longs or Shorts, open the GKD-BT Backtest, click the tab "Properties" and then insert a value of something like 10 orders into the "Pyramiding" settings. This will allow 10 orders to be opened at one time which should be enough to catch all possible Longs or Shorts.
Solo Confirmation Simple (Confirmation, Backtest)
1. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Simple"
1. Import the GKD-C indicator into the GKD-BT Backtest: "Input into Backtest"
2. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Solo Confirmation Simple"
Solo Confirmation Complex without Exits (Baseline, Volatility/Volume, Confirmation, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Complex"
4. Import the GKD-V indicator into the GKD-C indicator: "Input into C1 or Backtest"
5. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full wo/ Exits"
6. Import the GKD-C into the GKD-BT Backtest: "Input into Exit or Backtest"
Solo Confirmation Complex with Exits (Baseline, Volatility/Volume, Confirmation, Exit, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C indicator, change the "Confirmation Type" setting to "Solo Confirmation Complex"
4. Import the GKD-V indicator into the GKD-C indicator: "Input into C1 or Backtest"
5. Import the GKD-C indicator into the GKD-E indicator: "Input into Exit"
6. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full w/ Exits"
7. Import the GKD-E into the GKD-BT Backtest: "Input into Backtest"
Full GKD without Exits (Baseline, Volatility/Volume, Confirmation 1, Confirmation 2, Continuation, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C 1 indicator, change the "Confirmation Type" setting to "Confirmation 1"
4. Import the GKD-V indicator into the GKD-C 1 indicator: "Input into C1 or Backtest"
5. Inside the GKD-C 2 indicator, change the "Confirmation Type" setting to "Confirmation 2"
6. Import the GKD-C 1 indicator into the GKD-C 2 indicator: "Input into C2"
7. Inside the GKD-C Continuation indicator, change the "Confirmation Type" setting to "Continuation"
8. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full wo/ Exits"
9. Import the GKD-E into the GKD-BT Backtest: "Input into Exit or Backtest"
Full GKD with Exits (Baseline, Volatility/Volume, Confirmation 1, Confirmation 2, Continuation, Exit, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Chained"
2. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
3. Inside the GKD-C 1 indicator, change the "Confirmation Type" setting to "Confirmation 1"
4. Import the GKD-V indicator into the GKD-C 1 indicator: "Input into C1 or Backtest"
5. Inside the GKD-C 2 indicator, change the "Confirmation Type" setting to "Confirmation 2"
6. Import the GKD-C 1 indicator into the GKD-C 2 indicator: "Input into C2"
7. Inside the GKD-C Continuation indicator, change the "Confirmation Type" setting to "Continuation"
8. Import the GKD-C Continuation indicator into the GKD-E indicator: "Input into Exit"
9. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "GKD Full w/ Exits"
10. Import the GKD-E into the GKD-BT Backtest: "Input into Backtest"
Baseline + Volatility/Volume (Baseline, Volatility/Volume, Backtest)
1. Inside the GKD-V indicator, change the "Testing Type" setting to "Baseline + Volatility/Volume"
2. Inside the GKD-V indicator, make sure the "Signal Type" setting is set to "Traditional"
3. Import the GKD-B Baseline into the GKD-V indicator: "Input into Volatility/Volume or Backtest (Baseline testing)"
4. Inside the GKD-BT Backtest, change the setting "Backtest Special" to "Baseline + Volatility/Volume"
5. Import the GKD-V into the GKD-BT Backtest: "Input into C1 or Backtest"
6. Inside the GKD-BT Backtest, change the setting "Backtest Type" to "Full". For this backtest, you must test Longs and Shorts separately
7. To allow the system to open multiple orders at one time so you can test all Longs or Shorts, open the GKD-BT Backtest, click the tab "Properties" and then insert a value of something like 10 orders into the "Pyramiding" settings. This will allow 10 orders to be opened at one time which should be enough to catch all possible Longs or Shorts.
Requirements
Inputs
Chained: GKD-B Baseline
Solo: NA, no inputs
Baseline + Volatility/Volume: GKD-B Baseline
Outputs
Chained: GKD-C indicators Confirmation 1 or Solo Confirmation Complex
Solo: GKD-BT Backtest
Baseline + Volatility/Volume: GKD-BT Backtest
Additional features will be added in future releases.
Musashi_Fractal_Dimension === Musashi-Fractal-Dimension ===
This tool is part of my research on the fractal nature of the markets and understanding the relation between fractal dimension and chaos theory.
To take full advantage of this indicator, you need to incorporate some principles and concepts:
- Traditional Technical Analysis is linear and Euclidean, which makes very difficult its modeling.
- Linear techniques cannot quantify non-linear behavior
- Is it possible to measure accurately a wave or the surface of a mountain with a simple ruler?
- Fractals quantify what Euclidean Geometry can’t, they measure chaos, as they identify order in apparent randomness.
- Remember: Chaos is order disguised as randomness.
- Chaos is the study of unstable aperiodic behavior in deterministic non-linear dynamic systems
- Order and randomness can coexist, allowing predictability.
- There is a reason why Fractal Dimension was invented, we had no way of measuring fractal-based structures.
- Benoit Mandelbrot used to explain it by asking: How do we measure the coast of Great Britain?
- An easy way of getting the need of a dimension in between is looking at the Koch snowflake.
- Market prices tend to seek natural levels of ranges of balance. These levels can be described as attractors and are determinant.
Fractal Dimension Index ('FDI')
Determines the persistence or anti-persistence of a market.
- A persistent market follows a market trend. An anti-persistent market results in substantial volatility around the trend (with a low r2), and is more vulnerable to price reversals
- An easy way to see this is to think that fractal dimension measures what is in between mainstream dimensions. These are:
- One dimension: a line
- Two dimensions: a square
- Three dimensions: a cube.
--> This will hint you that at certain moment, if the market has a Fractal Dimension of 1.25 (which is low), the market is behaving more “line-like”, while if the market has a high Fractal Dimension, it could be interpreted as “square-like”.
- 'FDI' is trend agnostic, which means that doesn't consider trend. This makes it super useful as gives you clean information about the market without trying to include trend stuff.
Question: If we have a game where you must choose between two options.
1. a horizontal line
2. a vertical line.
Each iteration a Horizontal Line or a Square will appear as continuation of a figure. If it that iteration shows a square and you bet vertical you win, same as if it is horizontal and it is a line.
- Wouldn’t be useful to know that Fractal dimension is 1.8? This will hint square. In the markets you can use 'FD' to filter mean-reversal signals like Bollinger bands, stochastics, Regular RSI divergences, etc.
- Wouldn’t be useful to know that Fractal dimension is 1.2? This will hint Line. In the markets you can use 'FD' to confirm trend following strategies like Moving averages, MACD, Hidden RSI divergences.
Calculation method:
Fractal dimension is obtained from the ‘hurst exponent’.
'FDI' = 2 - 'Hurst Exponent'
Musashi version of the Classic 'OG' Fractal Dimension Index ('FDI')
- By default, you get 3 fast 'FDI's (11,12,13) + 1 Slow 'FDI' (21), their interaction gives useful information.
- Fast 'FDI' cross will give you gray or red dots while Slow 'FDI' cross with the slowest of the fast 'FDI's will give white and orange dots. This are great to early spot trend beginnings or trend ends.
- A baseline (purple) is also provided, this is calculated using a 21 period Bollinger bands with 1.618 'SD', once calculated, you just take midpoint, this is the 'TDI's (Traders Dynamic Index) way. The indicator will print purple dots when Slow 'FDI' and baseline crosses, I see them as Short-Term cycle changes.
- Negative slope 'FDI' means trending asset.
- Positive most of the times hints correction, but if it got overextended it might hint a rocket-shot.
TDI Ranges:
- 'FDI' between 1.0≤ 'FDI' ≤1.4 will confirm trend following continuation signals.
- 'FDI' between 1.6≥ 'FDI' ≥2.0 will confirm reversal signals.
- 'FDI' == 1.5 hints a random unpredictable market.
Fractal Attractors
- As you must know, fractals tend orbit certain spots, this are named Attractors, this happens with any fractal behavior. The market of course also shows them, in form of Support & Resistance, Supply Demand, etc. It’s obvious they are there, but now we understand that they’re not linear, as the market is fractal, so simple trendline might not be the best tool to model this.
- I’ve noticed that when the Musashi version of the 'FDI' indicator start making a cluster of multicolor dots, this end up being an attractor, I tend to draw a rectangle as that area as price tend to come back (I still researching here).
Extra useful stuff
- Momentum / speed: Included by checking RSI Study in the indicator properties. This will add two RSI’s (9 and a 7 periods) plus a baseline calculated same way as explained for 'FDI'. This gives accurate short-term trends. It also includes RSI divergences (regular and hidden), deactivate with a simple check in the RSI section of the properties.
- BBWP (Bollinger Bands with Percentile): Efficient way of visualizing volatility as the percentile of Bollinger bands expansion. This line varies color from Iced blue when low volatility and magma red when high. By default, comes with the High vols deactivated for better view of 'FDI' and RSI while all studies are included. DDWP is trend agnostic, just like 'FDI', which make it very clean at providing information.
- Ultra Slow 'FDI': I noticed that while using BBWP and RSI, the indicator gets overcrowded, so there is the possibility of adding only one 'FDI' + its baseline.
Final Note: I’ve shown you few ways of using this indicator, please backtest before using in real trading. As you know trading is more about risk and trade management than the strategy used. This still a work in progress, I really hope you find value out of it. I use it combination with a tool named “Musashi_Katana” (also found in TradingView).
Best!
Musashi
Lyapunov Hodrick-Prescott Oscillator w/ DSL [Loxx]Lyapunov Hodrick-Prescott Oscillator w/ DSL is a Hodrick-Prescott Channel Filter that is modified using the Lyapunov stability algorithm to turn the filter into an oscillator. Signals are created using Discontinued Signal Lines.
What is the Lyapunov Stability?
As soon as scientists realized that the evolution of physical systems can be described in terms of mathematical equations, the stability of the various dynamical regimes was recognized as a matter of primary importance. The interest for this question was not only motivated by general curiosity, but also by the need to know, in the XIX century, to what extent the behavior of suitable mechanical devices remains unchanged, once their configuration has been perturbed. As a result, illustrious scientists such as Lagrange, Poisson, Maxwell and others deeply thought about ways of quantifying the stability both in general and specific contexts. The first exact definition of stability was given by the Russian mathematician Aleksandr Lyapunov who addressed the problem in his PhD Thesis in 1892, where he introduced two methods, the first of which is based on the linearization of the equations of motion and has originated what has later been termed Lyapunov exponents (LE). (Lyapunov 1992)
The interest in it suddenly skyrocketed during the Cold War period when the so-called "Second Method of Lyapunov" (see below) was found to be applicable to the stability of aerospace guidance systems which typically contain strong nonlinearities not treatable by other methods. A large number of publications appeared then and since in the control and systems literature. More recently the concept of the Lyapunov exponent (related to Lyapunov's First Method of discussing stability) has received wide interest in connection with chaos theory . Lyapunov stability methods have also been applied to finding equilibrium solutions in traffic assignment problems.
In practice, Lyapunov exponents can be computed by exploiting the natural tendency of an n-dimensional volume to align along the n most expanding subspace. From the expansion rate of an n-dimensional volume, one obtains the sum of the n largest Lyapunov exponents. Altogether, the procedure requires evolving n linearly independent perturbations and one is faced with the problem that all vectors tend to align along the same direction. However, as shown in the late '70s, this numerical instability can be counterbalanced by orthonormalizing the vectors with the help of the Gram-Schmidt procedure (Benettin et al. 1980, Shimada and Nagashima 1979) (or, equivalently with a QR decomposition). As a result, the LE λi, naturally ordered from the largest to the most negative one, can be computed: they are altogether referred to as the Lyapunov spectrum.
The Lyapunov exponent "λ" , is useful for distinguishing among the various types of orbits. It works for discrete as well as continuous systems.
λ < 0
The orbit attracts to a stable fixed point or stable periodic orbit. Negative Lyapunov exponents are characteristic of dissipative or non-conservative systems (the damped harmonic oscillator for instance). Such systems exhibit asymptotic stability; the more negative the exponent, the greater the stability. Superstable fixed points and superstable periodic points have a Lyapunov exponent of λ = −∞. This is something akin to a critically damped oscillator in that the system heads towards its equilibrium point as quickly as possible.
λ = 0
The orbit is a neutral fixed point (or an eventually fixed point). A Lyapunov exponent of zero indicates that the system is in some sort of steady state mode. A physical system with this exponent is conservative. Such systems exhibit Lyapunov stability. Take the case of two identical simple harmonic oscillators with different amplitudes. Because the frequency is independent of the amplitude, a phase portrait of the two oscillators would be a pair of concentric circles. The orbits in this situation would maintain a constant separation, like two flecks of dust fixed in place on a rotating record.
λ > 0
The orbit is unstable and chaotic. Nearby points, no matter how close, will diverge to any arbitrary separation. All neighborhoods in the phase space will eventually be visited. These points are said to be unstable. For a discrete system, the orbits will look like snow on a television set. This does not preclude any organization as a pattern may emerge. Thus the snow may be a bit lumpy. For a continuous system, the phase space would be a tangled sea of wavy lines like a pot of spaghetti. A physical example can be found in Brownian motion. Although the system is deterministic, there is no order to the orbit that ensues.
For our purposes here, we transform the HP by applying Lyapunov Stability as follows:
output = math.log(math.abs(HP / HP ))
You can read more about Lyapunov Stability here: Measuring Chaos
What is. the Hodrick-Prescott Filter?
The Hodrick-Prescott (HP) filter refers to a data-smoothing technique. The HP filter is commonly applied during analysis to remove short-term fluctuations associated with the business cycle. Removal of these short-term fluctuations reveals long-term trends.
The Hodrick-Prescott (HP) filter is a tool commonly used in macroeconomics. It is named after economists Robert Hodrick and Edward Prescott who first popularized this filter in economics in the 1990s. Hodrick was an economist who specialized in international finance. Prescott won the Nobel Memorial Prize, sharing it with another economist for their research in macroeconomics.
This filter determines the long-term trend of a time series by discounting the importance of short-term price fluctuations. In practice, the filter is used to smooth and detrend the Conference Board's Help Wanted Index (HWI) so it can be benchmarked against the Bureau of Labor Statistic's (BLS) JOLTS, an economic data series that may more accurately measure job vacancies in the U.S.
The HP filter is one of the most widely used tools in macroeconomic analysis. It tends to have favorable results if the noise is distributed normally, and when the analysis being conducted is historical.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included:
Bar coloring
Alerts
Signals
Loxx's Expanded Source Types
OWRS VolatilililityBit of a fun indicator taking into the asset names and natural processes and also the fact that the crypto markets are (definitely) not run by weird occultists and naturalists. Looks for disturbances in price of these four key assets. Read into it what you will. Sometimes the clues are just in the names.
Things you will learn from this script:
1. Using security function to compare multiple assets in one indicator.
2. Using indexing to reference historic data.
3. Setting chart outputs such as color based on interrogation of a boolean.
4. To only go back 3-4 iterations of any repeatable sequence as chaos kicks in after 3.55 (Feigenbaum)
1. By extension only the last 3 or 4 candles are of any use in indicator creation.
2. I am almost definitely a pagan.
3. You were expecting this numbered list to go 1,2,3,4,5,6,7. na mate. Chaos.
A Better Fractal (Williams)DESCRIPTION:
This is a more advanced version of the classic Williams Fractal algo, using a looped barindex iterator to examine highs/lows.
You may choose ideal or regular fractals, along with the amount of bars (periods) used to calculate; the minimum being 3. Oddnums only.
Ideal fractals = fractals with each bar needing to be lower/higher than the preceding bar, with the midbar at the apex.
Regular fractals = the typical Williams fractal, wherein each bar only has to be lower/higher than the midbar (apex) only.
How to trade? Combine with other indicators and use breakout or reversal strategies, typically. Set buy/sell stops at the high/low of a fractal, for instance
... to trade the breakout when it occurs. Or, track momentum when a fractal prints and trade accordingly. Or perhaps trade with the alligator or 3 EMA.
Experiment with different types of fractals to achieve the desired result, with higher period fractals obviously offering more solid indication though with higher lag.
Note: A fractal does not print until n/2 (rounded down) bars after, where n = the period you chose.
JamesCart's Feigenbaum Constant/Rate Of Change indicatorThis is an indicator that compares the rate of change as a proportion to the Feigenbaum Constant (The black line). The green line is a positive divergence from the rate of change, the red is a negative divergence from the rate of change. When the Red line is on top and the green line is on the bottom, then that is a bearish trend. When the Green is on top and the red is on bottom, that is a bullish trend. The black line also helps indicate a general bullish or bearish trend based on how it moves.
When the lines "open up" that means a trend is beginning, when the lines close that means the trend is ending. This indicator is a powerful leading indicator and needs sensitive eyes. Every small movement needs to be given consideration.
Combo Backtest 123 Reversal & Fractal Chaos Oscillator This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
The value of Fractal Chaos Oscillator is calculated as the difference between
the most subtle movements of the market. In general, its value moves between
-1.000 and 1.000. The higher the value of the Fractal Chaos Oscillator, the
more one can say that it follows a certain trend – an increase in prices trend,
or a decrease in prices trend.
Being an indicator expressed in a numeric value, traders say that this is an
indicator that puts a value on the trendiness of the markets. When the FCO reaches
a high value, they initiate the “buy” operation, contrarily when the FCO reaches a
low value, they signal the “sell” action. This is an excellent indicator to use in
intra-day trading.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Fractal Chaos OscillatorThis is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
The value of Fractal Chaos Oscillator is calculated as the difference between
the most subtle movements of the market. In general, its value moves between
-1.000 and 1.000. The higher the value of the Fractal Chaos Oscillator, the
more one can say that it follows a certain trend – an increase in prices trend,
or a decrease in prices trend.
Being an indicator expressed in a numeric value, traders say that this is an
indicator that puts a value on the trendiness of the markets. When the FCO reaches
a high value, they initiate the “buy” operation, contrarily when the FCO reaches a
low value, they signal the “sell” action. This is an excellent indicator to use in
intra-day trading.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Fractal Chaos Bands This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
Stock market moves in a highly chaotic way, but at a larger scale, the movements
follow a certain pattern that can be applied to shorter or longer periods of time
and we can use Fractal Chaos Bands Indicator to identify those patterns. Basically,
the Fractal Chaos Bands Indicator helps us to identify whether the stock market is
trending or not. When a market is trending, the bands will have a slope and if market
is not trending the bands will flatten out. As the slope of the bands decreases, it
signifies that the market is choppy, insecure and variable. As the graph becomes more
and more abrupt, be it going up or down, the significance is that the market becomes
trendy, or stable. Fractal Chaos Bands Indicator is used similarly to other bands-indicator
(Bollinger bands for instance), offering trading opportunities when price moves above or
under the fractal lines.
The FCB indicator looks back in time depending on the number of time periods trader selected
to plot the indicator. The upper fractal line is made by plotting stock price highs and the
lower fractal line is made by plotting stock price lows. Essentially, the Fractal Chaos Bands
show an overall panorama of the price movement, as they filter out the insignificant fluctuations
of the stock price.
WARNING:
- For purpose educate only
- This script to change bars colors.
Advanced Fractal Dimension Index [DW]This is an experimental study based on Benoit Mandelbrot's fractal dimension concepts.
Fractal dimension is a ratio providing a statistical measure of complexity comparing how detail in a pattern changes with the scale at which it's measured.
The concept of a fractional or fractal dimension was derived from an unconventional approach to standard geometric definitions.
We all know the standard geometric rules of dimension: D=0 is a point, D=1 is a line, D=2 is a plane, and D=3 is a volume, based on the number of axes being occupied.
However, by taking a fractal geometric approach, we can define dimension like so:
N = s^-D , where N is the number of measurement segments, s is the scale factor, and D is the dimension of the object being measured.
This approach typifies conventional knowledge of dimensions as well. Here are some basic examples:
If we divide a line segment into 4 equal line segments, then we'd get 4 = (1/4)^-D. Solving for D, we get D=1, which is what we'd expect from a line.
If we divide a square into 16 equal squares, we'd be separating each line on the square into 4 pieces, so 16 = (1/4)^-D. Solving for D, we get D=2, which is what we'd expect from a square.
If we divide a cube into 64 equal cubes, we'd be separating each line on the cube into 4 pieces, so 64 = (1/4)^-D. Solving for D, we get D=3, which is what we'd expect from a cube.
The same approach can be applied to fractal objects, although admittedly it's less intuitive.
Let's say you use a stick to measure a curve, then you divide the stick into 3 equal segments and re-measure the length.
But rather than the re-measured curve showing a length of 3 of the smaller segments, it is actually 4 segments long.
This irregularity means that detail has increased as you scaled your measurement down, so the curve is dimensionally higher than the space it resides in.
In this example: 4 = (1/3)^-D. Solving for D, we get D=1.2619.
For a true fractal, this scaling of self-similar measurements would continue infinitely.
However, unlike true fractals, most real world phenomena exhibit limited fractal properties, in which they can be scaled down to some limited quantity.
Many forms of time series data (seismic data, ECG data, financial data, etc.) have been theoretically shown to have limited fractal properties.
Consequently, we can estimate fractal dimension from this data to get an approximate measure of how rough or convoluted the data stream is.
Financial data's fractal dimension is limited to between 1 and 2, so it can be used to roughly approximate the Hurst Exponent by the relationship H = 2 - D.
When D=1.5, data statistically behaves like a random walk. D above 1.5 can be considered more rough or "mean reverting" due to the increase in complexity of the series.
D below 1.5 can be considered more prone to trending due to the decrease in complexity of the series.
In this study, you are given the option to apply equalization (EQ) to the dataset before estimating dimension.
This enables you to transform your data and observe how its complexity changes as well.
Whether you want to give emphasis to some frequencies, isolate specific bands, or completely alter the shape of your waveform, EQ filtration makes for an interesting experience.
The default EQ preset in this script removes the low shelf, then attenuates low end and high end oscillations.
The dominant cyclical components (bands 3 - 5 on default settings) are passed at 100%, keeping emphasis on 8 to 64 sample per cycle oscillations.
In addition, if you're wanting a simpler filter process, or if you want a little extra, there are options included to pre and post smooth the data with 2 pole Butterworth LPFs.
The dimension estimation in this script works by measuring changes in detail using source's maximum range over a given lookback length.
In essence, it recursively updates its length parameter based on changes in range compared to the maximum over the lookback period, then uses the data to solve for D.
The FDI algorithm works on any length greater than 1. However, I didn't notice any particularly meaningful results with lookback lengths of 15 or less.
A custom color scheme is included in this script as well for FDI fill and bar colors.
The color scheme in this script is a multicolored thermal styled gradient.
The scale of gradient values is determined by the designated high and low dimension thresholds. These thresholds determine what range of values the gradient will focus on.
Values at the high threshold are the coolest and darkest, and values at the low threshold are the warmest and brightest.
Basically, the "trendier" the data is, the brighter and warmer the color will be.
Signals and alerts are included as well for crossovers on the high and low dimension thresholds.
These signals can also be externally linked to another script.
The output format is 1 for the trigger, and 0 otherwise. Basic boolean logic.
To integrate these signals with your script, simply use a source input and select the signal output from this script that you wish to use from the dropdown menu.
Fractal dimension is a powerful tool that can give valuable insight about the complexity and persistence / anti-persistence of price movements.
When used in conjunction with other analytical methods, it can prove to be a surprisingly beneficial tool to have in the arsenal.
-----------------------------------------------------
This is a premium script, and access is granted on an invite-only basis.
To gain access, get a copy of the indicator overview, or for additional inquiries, send me a direct message.
I look forward to hearing from you!
-----------------------------------------------------
General Disclaimer:
Trading stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument has large potential rewards, but also large potential risk.
You must be aware of the risks and be willing to accept them in order to invest in stocks, futures, Forex, options, ETFs or cryptocurrencies.
Don’t trade with money you can’t afford to lose.
This is neither a solicitation nor an offer to Buy/Sell stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument.
No representation is being made that any account will or is likely to achieve profits or losses of any kind.
The past performance of any trading system or methodology is not necessarily indicative of future results.
MAPS - LongShortThis script analyzes volume and momentum for different timeframes to spot opportunities for Longs or Shorts.
Please see below for access to indicators.
Volatility DMBefore anything, take notes of the script limitations :
1) The script has the setting : "Max_bars_back" set to 390. This is required to use dynamic length and an "internal clock"
*390 is the normal number of bars in a typical stock trading day.
2) The script requires volume data to work correctly
* I use a way to represent volatility that requires ( volume + price movement + time, no sma , no stdev)
Why ? Because:
HIGH-LOW = Fail to get gap information, fail to get volume information
TR/ATR = Fail to get volume information
STDEV = Not very good with dynamic length as it use SMA and fails when length <2
Conclusion: this script is basically limited to stock trading.
If I could set Max_bars_back to 23 400 this would even work better with a 1 second time frame as more data would be entered in the system.
The idea behind the script is that volatility exists in two different formats depending on how you observe the situation.
Remember your physics class? Light can be a wave or a particle depending of the situation.
Volatility seems to share a strange similar property.
Format 1) Instant volatility . (Ex. High - Low, TR )
Format 2) Systemic volatility (Ex. Dynamic ATR with variable length)
I then speculate 3 lines. (on both directions, + or -)
What if all transaction were 50% directional according to the instant volatility
What if all transaction were 100% directional according to the instant volatility
What if all transaction were 200% directional according to the instant volatility
sum(0,5*instant volatility , dynamic time)
sum(instant volatility , dynamic time)
sum(2*instant volatility , dynamic time)
This give you potential signals lines and support/resistance .
I then calculate the real price movement
sum(price movement, dynamic time)
Then you need to compare the real price movement VS if all transaction were 100% directional following the system volatility
dif=(sum price movement/sum volatility )*dynamic time
Voila.
If the movement is directional then it follows the system volatility .
If the movement is not directional then it goes back toward the Zero.
Inspirational image :
en.wikipedia.org
ChaosSN Label SignalThis signal indicator combines some key turning points including Fractals, Volume, Moving average and Momentum to try and pinpoint the moments a breakout or reversal is likely.
-Green/Red Arrows
Shows a possible breakout is pending. Place a long/short sell above or below the price line which is generated. Place a stop at a reasonable level as it's not guaranteed these breakouts will occur.
-Yellow Arrows
Shows a possible reversal is pending. Place a long/short sell above or below the price line which is generated. Place a stop at a reasonable level as it's not guaranteed these breakouts will occur.
Labels are also included to show possible rising/falling momentum as well as possible bullish/bearish/exhaustion candles.
ChaosVChaosV- Chaos Volume, is another Bill Williams' style indicator. It's essentially the Profitunity Candles, but in a Volume Bar setup. It incorporates MFI, to determine if a bar meets the Green, Squat, Fade or Fake requirements, as set by Bill Williams in his book Trading Chaos.
Gaussian Acceleration/Deceleration by KviateqBill Williams' AC (Acceleration/Deceleration), made using Gaussian-smoother Moving Averages and a 5-period EMA instead of the usual SMA.
Since Gaussian MA's are faster reacting than the typical SMAs values have been adjusted accordingly.
See also Gaussian Alligator and GaussianAO for a complete gaussian chaos trading system.
These scripts are made to honor Bill and his amazing work and my humble attempt at contributing to his work
Gaussian Awesome Oscillator by KviateqBill Williams' Awesome Oscillator, made using Gaussian-smoother Moving Averages.
Since Gaussian MA's are faster reacting than the typical SMAs values have been adjusted accordingly.
See also Gaussian Alligator and GaussianACDC for a complete gaussian chaos trading system.
These scripts are made to honor Bill and his amazing work and my humble attempt at contributing to his work
Gaussian Alligator by KviateqBill Williams' Alligator, made using Gaussian-smoother Moving Averages.
Since Gaussian MA's are faster reacting than the typical SMAs values have been adjusted accordingly.
See also GaussianAO and GaussianACDC for a complete gaussian chaos trading system.
These scripts are made to honor Bill and his amazing work and my humble attempt at contributing to his work
Chaos Fibonacci Bollinger Bands by ZekisBollinger Bands calculated with a Simple Moving Average and offsets with Fibonacci Retracement values (0.236; 0.382; 0.5; 0.618; 0.784 and 1) for a better support and resistance view, moves and a lot of TA (support and resistance, pivot points, reverse, breakouts...etc)
I colored each part of Fib. to see them clearly
Standard deviation and lenght of BB can be adjusted
Enjoy!
@Zekis
BullTrading Intraday StopHunt Indicator Phycologically traders tend to sell on lows and buy on highs. BullTrading Intraday StopHunt Indicator is designed to help you avoid such situations by monitoring the market for intraday trading setups.
The indicator plots a "Fractal Envelope © " containing the most significant Support and Resistance levels for analysis and entry level selection.
Trend filtering is provided by a MTF P-SAR (SAR will avoid repainting false signals).
The BullTrading Chaos Trend Wave is used instead the Alligator to trade fractals.
BullTrading Intraday StopHunt Indicator will provide 3 types of signals:
First one is a swing/intraday signal, it will alert you when the price is located at a very sensitive level (buy or sell) filtered by trend. If you check the indicator after the close of the day you can even know this exact level in advance (plot Red or Lime color).
Second signal will alert you the Chaos Trend Wave Moving Average Crossovers filtered by price position (related to the Fractal Envelope) and mayor trend.
Third signal is a scalping signal, it will alert you all the fractal breakouts filtered by price position (related to the Fractal Envelope) and mayor trend.
You will be amazed the huge amount of trade opportunities for a given week trading only one financial instrument.
Obviously the indicator is not perfect and will plot few false signals on mayor trend reversals or big price manipulations. AVOID THE TRAP BY WAITING THE PRICE USING BUY LIMIT AND SELL LIMIT ORDERS.
NOTE: This indicator works on any timeframe, but standard settings are calibrated for 15' charts.
