[cache_that_pass] 1m 15m Function - Weighted Standard DeviationTradingview Community,
As I progress through my journey, I have come to the realization that it is time to give back. This script isn't a life changer, but it has the building blocks for a motivated individual to optimize the parameters and have a production script ready to go.
Credit for the indicator is due to @rumpypumpydumpy
I adapted this indicator to a strategy for crypto markets. 15 minute time frame has worked best for me.
It is a standard deviation script that has 3 important user configured parameters. These 3 things are what the end user should tweak for optimum returns. They are....
1) Lookback Length - I have had luck with it set to 20, but any value from 1-1000 it will accept.
2) stopPer - Stop Loss percentage of each trade
3) takePer - Take Profit percentage of each trade
2 and 3 above are where you will see significant changes in returns by altering them and trying different percentages. An experienced pinescript programmer can take this and build on it even more. If you do, I ask that you please share the script with the community in an open-source fashion.
It also already accounts for the commission percentage of 0.075% that Binance.US uses for people who pay fees with BNB.
How it works...
It calculates a weighted standard deviation of the price for the lookback period set (so 20 candles is default). It recalculates each time a new candle is printed. It trades when price lows crossunder the bottom of that deviation channel, and sells when price highs crossover the top of that deviation channel. It works best in mid to long term sideways channels / Wyckoff accumulation periods.
Regression
Ripple (XRP) Model PriceAn article titled Bitcoin Stock-to-Flow Model was published in March 2019 by "PlanB" with mathematical model used to calculate Bitcoin model price during the time. We know that Ripple has a strong correlation with Bitcoin. But does this correlation have a definite rule?
In this study, we examine the relationship between bitcoin's stock-to-flow ratio and the ripple(XRP) price.
The Halving and the stock-to-flow ratio
Stock-to-flow is defined as a relationship between production and current stock that is out there.
SF = stock / flow
The term "halving" as it relates to Bitcoin has to do with how many Bitcoin tokens are found in a newly created block. Back in 2009, when Bitcoin launched, each block contained 50 BTC, but this amount was set to be reduced by 50% every 210,000 blocks (about 4 years). Today, there have been three halving events, and a block now only contains 6.25 BTC. When the next halving occurs, a block will only contain 3.125 BTC. Halving events will continue until the reward for minors reaches 0 BTC.
With each halving, the stock-to-flow ratio increased and Bitcoin experienced a huge bull market that absolutely crushed its previous all-time high. But what exactly does this affect the price of Ripple?
Price Model
I have used Bitcoin's stock-to-flow ratio and Ripple's price data from April 1, 2014 to November 3, 2021 (Daily Close-Price) as the statistical population.
Then I used linear regression to determine the relationship between the natural logarithm of the Ripple price and the natural logarithm of the Bitcoin's stock-to-flow (BSF).
You can see the results in the image below:
Basic Equation : ln(Model Price) = 3.2977 * ln(BSF) - 12.13
The high R-Squared value (R2 = 0.83) indicates a large positive linear association.
Then I "winsorized" the statistical data to limit extreme values to reduce the effect of possibly spurious outliers (This process affected less than 4.5% of the total price data).
ln(Model Price) = 3.3297 * ln(BSF) - 12.214
If we raise the both sides of the equation to the power of e, we will have:
============================================
Final Equation:
■ Model Price = Exp(- 12.214) * BSF ^ 3.3297
Where BSF is Bitcoin's stock-to-flow
============================================
If we put current Bitcoin's stock-to-flow value (54.2) into this equation we get value of 2.95USD. This is the price which is indicated by the model.
There is a power law relationship between the market price and Bitcoin's stock-to-flow (BSF). Power laws are interesting because they reveal an underlying regularity in the properties of seemingly random complex systems.
I plotted XRP model price (black) over time on the chart.
Estimating the range of price movements
I also used several bands to estimate the range of price movements and used the residual standard deviation to determine the equation for those bands.
Residual STDEV = 0.82188
ln(First-Upper-Band) = 3.3297 * ln(BSF) - 12.214 + Residual STDEV =>
ln(First-Upper-Band) = 3.3297 * ln(BSF) – 11.392 =>
■ First-Upper-Band = Exp(-11.392) * BSF ^ 3.3297
In the same way:
■ First-Lower-Band = Exp(-13.036) * BSF ^ 3.3297
I also used twice the residual standard deviation to define two extra bands:
■ Second-Upper-Band = Exp(-10.570) * BSF ^ 3.3297
■ Second-Lower-Band = Exp(-13.858) * BSF ^ 3.3297
These bands can be used to determine overbought and oversold levels.
Estimating of the future price movements
Because we know that every four years the stock-to-flow ratio, or current circulation relative to new supply, doubles, this metric can be plotted into the future.
At the time of the next halving event, Bitcoins will be produced at a rate of 450 BTC / day. There will be around 19,900,000 coins in circulation by August 2025
It is estimated that during first year of Bitcoin (2009) Satoshi Nakamoto (Bitcoin creator) mined around 1 million Bitcoins and did not move them until today. It can be debated if those coins might be lost or Satoshi is just waiting still to sell them but the fact is that they are not moving at all ever since. We simply decrease stock amount for 1 million BTC so stock to flow value would be:
BSF = (19,900,000 – 1.000.000) / (450 * 365) =115.07
Thus, Bitcoin's stock-to-flow will increase to around 115 until AUG 2025. If we put this number in the equation:
Model Price = Exp(- 12.214) * 114 ^ 3.3297 = 36.06$
Ripple has a fixed supply rate. In AUG 2025, the total number of coins in circulation will be about 56,000,000,000. According to the equation, Ripple's market cap will reach $2 trillion.
Note that these studies have been conducted only to better understand price movements and are not a financial advice.
NEXT Regressive VWAPOverview:
This version of the Volume-Weighted Average Price (VWAP) indicator features an extended algorithm, which, in addition to volume and price, also incorporates regression analysis. The result is a more responsive, often leading VWAP slope with a degree of statistical predictability built in. Just like with the original VWAP, NEXT Regressive VWAP offers two optional Standard Deviation bands that parallel it. These can be set to any deviation level, with the default being 1 and -1, indicating one standard deviation above and one below Regressive VWAP, respectively.
Below is a screenshot comparing NEXT Regressive VWAP (green) to the original VWAP (blue) on CME_MINI:ES1! M3 chart.
Application and Strategy Ideas:
Price above NEXT Regressive VWAP is interpreted to have a bullish bias, and below, bearish. You can use TradingView's native Set Alert functionality to be notified, in real-time, when price crosses Regressive VWAP, and/or any of its standard deviation bands. Another popular "probability play" strategy is to scalp price when it crosses under the upper band (short) and crosses over the lower band (long). The screenshot below visualizes such a strategy on NASDAQ:QQQ M1 chart:
Input Parameters:
There are 3 groups of input.
Regression Settings
Length - controls the length of time (in bars) for regression analysis with higher values yielding smoother, more responsive values.
Regression Weighting - controls the degree of regression analysis incorporated into VWAP, with 5 being average, 0-4 less, 6-10 more. The higher the value, the more responsive the Regressive VWAP curve.
VWAP Settings
Anchor Period - controls the origin of VWAP calculations, start of session being the default.
Source - data used for calculating the VWAP, typically HLC/3, but can be used with other price formats and data sources as well.
Offset - shifting of the VWAP line forward (+) or backward (-).
Standard Deviation Bands Settings
Calculate Bands - checking this will add 2 bands, each equidistant (by the amount of Multiplier) from the NEXT Regressive VWAP line.
Bands Multiplier - standard deviation multiplier, with 1 being the default
Signals and Alerts:
Here is how to set price (close) crossing NEXT Regressive VWAP alerts: open a chart, attach NEXT Regressive VWAP, and right-click on chart -> Add Alert. Condition: Symbol e.g. ES (close) >> Crossing >> Regressive VWAP >> VWAP >> Once Per Bar Close.
Polynomial Regression Style Examplejust a example on how to edit line style on the output of the polynomial regression library..
Nadaraya-Watson Envelope [LuxAlgo]This indicator builds upon the previously posted Nadaraya-Watson smoothers. Here we have created an envelope indicator based on Kernel Smoothing with integrated alerts from crosses between the price and envelope extremities. Unlike the Nadaraya-Watson estimator, this indicator follows a contrarian methodology.
Please note that by default this indicator can be subject to repainting. Users can use a non-repainting smoothing method available from the settings. The triangle labels are designed so that the indicator remains useful in real-time applications.
🔶 USAGE
🔹 Non Repainting
This tool can outline extremes made by the prices. This is achieved by estimating the underlying trend in the price, then calculating the mean absolute deviations from it, the obtained result is added/subtracted to the estimated underlying trend.
The non-repainting method estimates the underlying trend in price using an "endpoint Nadaraya-Watson estimator", and would return similar results to more classical band indicators.
🔹 Repainting
The repainting method makes use of the Nadaraya-Watson estimator to estimate the underlying trend in the price. The construction of the band extremities is the same as in the non-repainting method.
We can expect the price to reverse when crossing one of the envelope extremities. Crosses between the price and the envelopes extremities are indicated with triangles on the chart.
For real-time applications, triangles are always displayed when a cross occurs and remain displayed at the location it first appeared even if the cross is no longer visible after a recalculation of the envelope.
By popular demand, we have integrated alerts for this indicator from the crosses between the price and the envelope extremities. However, we do not recommend this precise method to be used alone or for solely real-time applications. We do not have data supporting the performance of this tool over more classical bands/envelope/channels indicators.
🔶 SETTINGS
Bandwidth: Controls the degree of smoothness of the envelopes, with higher values returning smoother results.
Mult: Controls the envelope width.
Source: Input source of the indicator.
Repainting Smoothing: Determine if a repainting or non-repainting method should be used for the calculation of the indicator.
🔶 RELATED SCRIPTS
For more information on the Nadaraya-Watson estimator see:
FunctionPolynomialRegressionLibrary "FunctionPolynomialRegression"
TODO:
polyreg(sample_x, sample_y) Method to return a polynomial regression channel using (X,Y) sample points.
Parameters:
sample_x : float array, sample data X points.
sample_y : float array, sample data Y points.
Returns: tuple with:
_predictions: Array with adjusted Y values.
_max_dev: Max deviation from the mean.
_min_dev: Min deviation from the mean.
_stdev/_sizeX: Average deviation from the mean.
draw(sample_x, sample_y, extend, mid_color, mid_style, mid_width, std_color, std_style, std_width, max_color, max_style, max_width) Method for drawing the Polynomial Regression into chart.
Parameters:
sample_x : float array, sample point X value.
sample_y : float array, sample point Y value.
extend : string, default=extend.none, extend lines.
mid_color : color, default=color.blue, middle line color.
mid_style : string, default=line.style_solid, middle line style.
mid_width : int, default=2, middle line width.
std_color : color, default=color.aqua, standard deviation line color.
std_style : string, default=line.style_dashed, standard deviation line style.
std_width : int, default=1, standard deviation line width.
max_color : color, default=color.purple, max range line color.
max_style : string, default=line.style_dotted, max line style.
max_width : int, default=1, max line width.
Returns: line array.
log-log Regression From ArraysCalculates a log-log regression from arrays. Due to line limits, for sets greater than the limit, only every nth value is plotted in order to cover the entire set.
Exponential Regression From ArraysCalculates an exponential regression from arrays. Due to line limits, for sets greater than the limit, only every nth value is plotted in order to cover the entire set.
Nadaraya-Watson Smoothers [LuxAlgo]The following tool smoothes the price data using various methods derived from the Nadaraya-Watson estimator, a simple Kernel regression method. This method makes use of the Gaussian kernel as a weighting function.
Users have the option to use a non-repainting as well as a repainting method, see the USAGE section for more information.
🔶 USAGE
🔹 Non Repainting
When Repainting Smoothing is disabled the returned indicator acts similarly to a regular causal moving average. This result could be described as an "endpoint Nadaraya-Watson estimator".
Unlike a regular moving average whose degree of smoothness is commonly determined by the length of its calculation window, the degree of smoothness of the proposed indicator is determined by the bandwidth setting, with a higher value returning smoother results.
In the above chart, a bandwidth value of 50 is used. An increasing value of the smoother is indicative of an uptrend, while a decreasing value is indicative of a downtrend.
🔹 Repainting
Non-causal smoothing methods have found low support from technical analysts because they tend to repaint. Yet, they can provide powerful insights such as estimating underlying trends in the price as well as seeing how far prices deviate from them. They can also make drawing certain patterns easier and can help see underlying structures in the price more clearly.
Using higher bandwidth values allows for estimating longer-term trends in the price.
Triangular labels highlight points where the direction of the estimator change. This allows for the identification of tops and bottoms in the underlying trend which can be compared to the actual price tops and bottoms.
Note that multiple labels can appear in real time, highlighting real-time changes in the estimator's direction. The most recent label on a series of labels is the first to appear. This can eventually be useful for the real-time predictive application of the estimator. However, it is not a usage we particularly recommend.
🔶 DETAILS
The Nadaraya-Watson estimator can be described as a series of weighted averages using a specific normalized kernel as a weighting function. For each point of the estimator at time t , the peak of the kernel is located at time t , as such the highest weights are attributed to values neighboring the price located at time t .
A lower bandwidth value would contribute toward a more important weighting of the price at a precise point and would as such less smooth results. In the case where our bandwidth is so small that the resulting kernel is just an impulse, we would get the raw price back.
However, when the bandwidth is sufficiently large, prices would be weighted similarly, thus resulting in a result closer to the price mean.
It can be interesting to note that due to the nature of the estimator and its weighting procedure, real-time results would not deviate drastically for points in the estimator near the center of the calculation window.
🔶 SETTINGS
Bandwidth : controls the bandwidth of the Gaussian kernel, with higher values returning smoother results.
Src : Input source of the kernel regression.
Repainting Smoothing : Determine if the smoothing method should repaint or not. If disabled the "endpoint Nadaraya-Watson estimator" is returned.
Liquidity Rainbow - Trillion ResearchThis indicator uses regression along with RSI and moving averages from multiple time frames to help you visualize the market in a single view. After learning the notations, you will be able to identify pockets of liquidity and determine high/low probability price zones without drawing a single line.
Booster symbols help confirm short term trends and breakouts based off of two waveform functions, one long period, the other with a much shorter period. You get the buy signal that everyone else sees plus the confirmation!
This is a system that is not fully developed, PNL is not available yet. Strategy version is coming soon, still back testing.
I am tuning this model for crypto specifically, although it works for anything with a price chart.
2 EMAs (configurable to MA)
Dragonskin - RGB circle plots eMA
Rainbow - RGB area plots eMA
+When you see the rainbow appear it means that the price is above the slowest ema baseline. Generally bullish as price tends to ride the rainbow. Ideally, you will see a white cloud at the origin.
-When you see white step line cutting into the upper colors of the rainbow.
Once the price has traded below the rainbow for the FIRST time, not just wicked. You can set a target that's just above the previous high bodys above the rainbow. Do not sell the dip, let the floppers flop.
The second time price cuts down through a thick rainbow is usually bearish .
What makes me so sure? Liquidity
In order to be successful, we need to understand liquidity, the juiciest pockets of profit.
I will reveal more of the strategy in the second script.
For now, use:
SUN symbol - Notice how the price always seems to come back and sweep up any SUNs that get left behind (up and down) this is a liquidity nugget
CLOUD(s) indicators of support. Meaning that on ema trend we expect a lower price but each time that happens, it gets bought up above baseline. weak->strong (little gray - light blue - white)
LIGHTNING indicator of resistance. Meaning the price is not being allowed to recover, each time it rises above baseline, it is sold down again.
YELLOW CROSS - Classically known as a whale manipulation indicator. It tends to indicate a strong bearish move incoming or the reversal of an ongoing bearish move. There's dumping. "Get ready something is happening" indicator.
HEARTS = BUY
SPADES = Buy
CLUBS = Sell
DIAMONDS = SELL
*do not use these during periods of consolidation. consolidation is a period when the price swings in both directions but not too much. In a narrow range the indicators can pop up.
Why does this happen?
Short periods, during which exchanges stabilize the prices, are necessary for the redistribution of assets over the course of trading. Sometimes they happen multiple times a week and can last 24 or 48hours. Also it is a great time to eat up algo traders and that's why you'll see noise.
You want to focus on the period immediately following a consolidations. Don't rush it, they really do take 20 hours+
If you realize that you are in one of these consolidation ranges, limit order the tips of the wicks, nothing in the middle. There is not much profit here but also there is minimal risk.
If you're confirmed in a consolidation, exchanges will work to buoy the price to the appropriate mark price even if there is a big buy/sell order. A lot of time price will go up the congruent amount afterwards to compensate the toxic vwap .
I hope this helps people see the bigger picture and become even more successful with bigger gains.
I've tested this on all the major cryptos. Bitcoin BTC Ethereum ETH HEX
Honestly, I have tested very few stonks with this, later.
-Market Enemy
Linear Regression & RSI Multi-Function Screener with Table-LabelHi fellow traders..
Happy to share a Linear Regression & RSI Multi-Function Custom Screener with Table-Labels...
The Screener scans for Linear Regression 2-SD Breakouts and RSI OB/OS levels for the coded tickers and gives Summary alerts
Uses Tables (dynamica resizing) for the scanner output instead of standard labels!
This Screener cum indicator collection has two distinct objectives..
1. Attempt re-entry into trending trades.
2. Attempt Counter trend trades using linear regression , RSI and Zigzag.
Briefly about the Screener functions..
a. It uses TABLES as Labels a FIRST for any Screener on TV.
b. Tables dynamically resize based on criteria..
c. Alerts for breakouts of the UPPER and the LOWER regression channels.(2 SD)
d. In addition to LinReg it also Screens RSI for OB/OS levels so a multifunction Screener.
e. Of course has the standard summary Alerts and programmable format for Custom functions.
f. Uses only the inbuilt Auto Fib and Lin Reg code for the screener.(No proprietary stuff)
g. The auto Zigzag code is derived(Auto fib).
Question what are all these doing in a single screener ??
ZigZag is very useful in determining Trend Up or Down from one Pivot to another.
So Once you have a firm view of the Current Trend for your chosen timeframe and ticker…
We can consider few possible trading scenarios..
a. Re-entry in an Up Trend - Combination of OS Rsi And a Lower Channel breach followed by a re-entry back into the regression channel CAN be used as an effective re-entry.
b. Similarily one can join a Down Trend on OB Rsi and Upper Channel line breach followed by re-entry into the regression channel.
If ZigZag signals a range-bound market, bound within channel lines then the Upper breakout can be used to Sell and vice-versa!
In short many possibilities for using these functions together with Scanner and Alerts.
This facilitates timely PROFITABLE Trending and Counter trend opportunities across multiple tickers.
You must give a thorough READ to the various available tutorials on ZigZag / Regression and Fib retracements before attempting counter trend trades using these tools!!
A small TIP – Markets are sideways or consolidating 70% of the time!!
Acknowledgements: - Thanks a lot DGTRD for the Auto ZigZag code and also for the eagerness to help wherever possible..Respect!!
Disclaimer: The Alerts and Screener are just few tools among many and not any kind of Buy/Sell recommendations. Unless you have sufficient trading experience please consult a Financial advisor before investing real money.
*The alerts are set for crossovers however for viewing tickers trading above or below the channel use code in line 343 and 344 after setting up the Alerts!
** RSI alerts are disabled by default to avoid clutter, but if needed one can activate code lines 441,442,444 and 445
Wish you all, Happy Profitable Trading!
Log Scale Linear RegressionThis indicator is basically the standard linear regression but adjusted to be suitable for log scale.
You can use 2 different standard deviation values, choose the data source and lookback length.
The colors are chosen directly on the main menu.
Enjoy!
Multiple Regression Polynomial ForecastEXPERIMENTAL:
Forecasting using a polynomial regression over the estimates of multiple linear regression forecasts.
note: on low data the estimates are skewd away of initial value, i added the i_min_estimate option in to try curve this issue with limited success "o_o.
Bitcoin Logarithmic Regression RainbowI know there are a lot of BTC rainbows out there, I just wanted to publish my version with my fittings to the BTC price.
The grey channel at the bottom encloses the March 2020 Corona dump.
For best experience USE WEEKLY TIMEFRAME .
Mayfair Advanced Regressions 1.0This indicator maps two regressions.
The outer regression (green straight lines in the chart) tracks the main trend. It save you from working out your own trend channels, BUT it does move with the price, so it is different from a static channel. You can use it as a template for drawing static channels though.
The inner regression (the curved lines) is a parabolic regression. It shows the shorter term trend within the outer trend. This helps traders to judge when it is right or wrong to take a position on the edge of the main regression, based on whether the inner regression is indicating an acceleration out of the channel, or is shaping to go with the main trend.
We find it works best if there is a clear trend. If the market is not trending, then there isn't much point using a trend analysis tool like this.
Like all indicators, it is not perfect, and you should never rely on one indicator in any situation.
Ethereum Logarithmic Growth Curves & ZonesThis script was modified to fit ethereum logarithmic pricing action.
Robust Channel [tbiktag]Introducing the Robust Channel indicator.
This indicator is based on a remarkable property of robust statistics , namely, the resistance to the presence of data points that deviate significantly from the established trend (generally speaking, outliers ). Being outlier-resistant, the Robust Channel indicator “remembers” a pre-existing trend and thus exhibits a very peculiar "lag" in case of a sharp price change. This allows high-confidence identification of such price actions as a trend reversal, range break, pullback, etc.
In the case of trending and range-bound market conditions, the price remains within the channel most of the time, fluctuating around the central line.
Technical details
The central line is calculated using the repeated median slope algorithm. For each data point in a lookback window of a user-specified Length , this method calculates the median slope of the lines that connect that point to all other points inside the window. The overall median of these median slopes is then calculated and used as an estimate of the trend slope. The algorithm is very efficient as it uses an on-the-fly procedure to update the array containing the slopes (new data pushed - old data removed).
The outer line is then calculated as the central line plus the Length -period standard deviation of the price data multiplied by a user-defined Channel Width Factor . The inner line is defined analogously below the central line.
Usage
As a stand-alone indicator, the Robust Channel can be applied similarly to the Bollinger Bands and the Keltner Channel:
A close above the outer line can be interpreted as a bullish signal and a close below the inner line as a bearish signal.
Likewise, a return to the channel from below after a break may serve as a bullish signal, while a return from above may indicate bearish sentiment.
Robust Channel can be also used to confirm chart patterns such as double tops and double bottoms.
If you like this indicator, feel free to leave your feedback in the comments below!
Matrix Library (Linear Algebra, incl Multiple Linear Regression)What's this all about?
Ever since 1D arrays were added to Pine Script, many wonderful new opportunities have opened up. There has been a few implementations of matrices and matrix math (most notably by TradingView-user tbiktag in his recent Moving Regression script: ). However, so far, no comprehensive libraries for matrix math and linear algebra has been developed. This script aims to change that.
I'm not math expert, but I like learning new things, so I took it upon myself to relearn linear algebra these past few months, and create a matrix math library for Pine Script. The goal with the library was to make a comprehensive collection of functions that can be used to perform as many of the standard operations on matrices as possible, and to implement functions to solve systems of linear equations. The library implements matrices using arrays, and many standard functions to manipulate these matrices have been added as well.
The main purpose of the library is to give users the ability to solve systems of linear equations (useful for Multiple Linear Regression with K number of independent variables for example), but it can also be used to simulate 2D arrays for any purpose.
So how do I use this thing?
Personally, what I do with my private Pine Script libraries is I keep them stored as text-files in a Libraries folder, and I copy and paste them into my code when I need them. This library is quite large, so I have made sure to use brackets in comments to easily hide any part of the code. This helps with big libraries like this one.
The parts of this script that you need to copy are labeled "MathLib", "ArrayLib", and "MatrixLib". The matrix library is dependent on the functions from these other two libraries, but they are stripped down to only include the functions used by the MatrixLib library.
When you have the code in your script (pasted somewhere below the "study()" call), you can create a matrix by calling one of the constructor functions. All functions in this library start with "matrix_", and all constructors start with either "create" or "copy". I suggest you read through the code though. The functions have very descriptive names, and a short description of what each function does is included in a header comment directly above it. The functions generally come in the following order:
Constructors: These are used to create matrices (empy with no rows or columns, set shape filled with 0s, from a time series or an array, and so on).
Getters and setters: These are used to get data from a matrix (like the value of an element or a full row or column).
Matrix manipulations: These functions manipulate the matrix in some way (for example, functions to append columns or rows to a matrix).
Matrix operations: These are the matrix operations. They include things like basic math operations for two indices, to transposing a matrix.
Decompositions and solvers: Next up are functions to solve systems of linear equations. These include LU and QR decomposition and solvers, and functions for calculating the pseudo-inverse or inverse of a matrix.
Multiple Linear Regression: Lastly, we find an implementation of a multiple linear regression, including all the standard statistics one can expect to find in most statistical software packages.
Are there any working examples of how to use the library?
Yes, at the very end of the script, there is an example that plots the predictions from a multiple linear regression with two independent (explanatory) X variables, regressing the chart data (the Y variable) on these X variables. You can look at this code to see a real-world example of how to use the code in this library.
Are there any limitations?
There are no hard limiations, but the matrices uses arrays, so the number of elements can never exceed the number of elements supported by Pine Script (minus 2, since two elements are used internally by the library to store row and column count). Some of the operations do use a lot of resources though, and as a result, some things can not be done without timing out. This can vary from time to time as well, as this is primarily dependent on the available resources from the Pine Script servers. For instance, the multiple linear regression cannot be used with a lookback window above 10 or 12 most of the time, if the statistics are reported. If no statistics are reported (and therefore not calculated), the lookback window can usually be extended to around 60-80 bars before the servers time out the execution.
Hopefully the dev-team at TradingView sees this script and find ways to implement this functionality diretly into Pine Script, as that would speed up many of the operations and make things like MLR (multiple linear regression) possible on a bigger lookback window.
Some parting words
This library has taken a few months to write, and I have taken all the steps I can think of to test it for bugs. Some may have slipped through anyway, so please let me know if you find any, and I'll try my best to fix them when I have time to do so. This library is intended to help the community. Therefore, I am releasing the library as open source, in the hopes that people may improving on it, or using it in their own work. If you do make something cool with this, or if you find ways to improve the code, please let me know in the comments.
Linear Regression CandlesThere are many linear regression indicators out there, most of them draw lines or channels, but this one actually draws a chart.
Moving Regression Band Breakout strategyFollowing the introduction of the Moving Regression Prediction Bands indicator (see link below), I'd like to propose how to utilize it in a simple band breakout strategy :
Go long after the candle closes above the upper band . The lower band (alternatively, the lower band minus the 14-period ATR or the central line ) will serve as a support line .
Exit as soon as the candle closes below the support line .
To manage the risk of false breakouts, a fixed stop loss is set to the value of the support line at the time of opening a position. When the support line moves above the position opening price, shift the stop loss to breakeven.
The same logic but in reverse applies to short positions.
As an option, it is possible to allow long entries only when the slope of the Moving Regression curve is positive (and short entries when the slope is negative).
Model parameters:
Length and Polynomial Order define the lag and smoothness of the model.
Multiplier specifies the width of the channel.
As the default model parameter values, I set those that I found to provide optimal risk / reward ratio on the daily timeframe (for both trending and range-bound market). However, the settings are very flexible and can be well-adjusted to particular market conditions. Feel free to play around and leave feedback in the comments!
Here's the original Moving Regression Prediction Bands script:
Moving Regression Prediction BandsIntroducing the Moving Regression Prediction Bands indicator.
Here I aimed to combine the principles of traditional band indicators (such as Bollinger Bands), regression channel and outlier detection methods. Its upper and lower bands define an interval in which the current price was expected to fall with a prescribed probability, as predicted by the previous-step result of the local polynomial regression (for the original Moving Regression script, see link below).
Algorithm
1. At every time step, the script performs local polynomial regression of the sample data within the lookback window specified by the Length input parameter.
2. The fitted polynomial is used to construct the Moving Regression time series as well as to extrapolate data, that is, to predict the next data point ( MRPrediction ).
3. The accuracy of local interpolation is estimated by means of the root-mean-square error ( RMSE ), that is, the deviation between the fitted polynomial and the observed values.
4. The MRPrediction and RMSE values calculated for the previous bar are then used to build the upper and lower bands , which I define as follows:
Upper Band = MRPrediction_prev + Multiplier *( RMSE_prev )
Lower Band = MRPrediction_prev - Multiplier *( RMSE_prev )
Here the Multiplier is a user-defined parameter that should be interpreted as a quantile in the standard normal distribution (the default value of 2.0 roughly corresponds to the 95% prediction interval).
To visualize the central line , the script offers the following options:
Previous-Period MR Prediction: MRPrediction_prev time series from the above equation.
MR: Conventional Moving Regression time series.
Ribbon: “Previous-Period MR Prediction” and “MR” curves plotted together and colored according to their relative value (green if MR > Previous MR Prediction; red otherwise).
Usage
My original idea was to use the band breakouts as potential trading signals. For example, the price crossing above the upper band is a bullish signal , being a potential sign that price is gaining momentum and is out of a previously predicted trend. The exit signal could be the crossing under the lower band or under the central line.
However, be aware that it is an experimental indicator, so you might fin some better strategies.
Feel free to play around!
Valero Logarithmic RegressionBTCUSD Logarithmic Regression
Inspired by: trolololo & Über Holger.
Make sure you have "log" and "auto" turned ON!
BLUE: BUY!
GREEN: ACCUMULATE
YELLOW: HODL!
ORANGE: FOMO / IS THIS A BUBBLE?
LIGHT RED: SELL!
RED: MAXIMUM BUBBLE TERRITORY
My new BTC log curveThis is my new logarithmic regression curve to the USD/BTC price chart. It is based on a new, very simple equation: y = (e^b)*(x^a), where x is number of days since the Genesis block, a and b are parameters set by the user. Also included is an upper regression curve that is fit to the peaks of each Bitcoin cycle; no fundamental analysis went into making these lines, they are merely fits to the data, so it should not be expected that they can be used to predict tops and bottoms. The upper regression curve is the product of the support curve (lower curve) and two other factors: a constant, and an exponential decay. The constant and the decay factors are parameters that can be set by the user.
