Bitcoin Logarithmic Fractal Growth Model By ARUDDThis model, which I'm calling the Logarithmic Fractal Growth Mode (L.F.G) , uses Bitcoin's mathematical monetary policy to evaluate the future possible price valuation.
It takes into account fractal (and logarithmic) growth as well as how those who hold bitcoins might react to certain events such as changes in supply and demand. It also shows that it is mathematically logical that someday it must become stable.
The information gained from knowing this helps people make more informed decisions when buying bitcoin and thinking of its future possibilities.
The model can serve as some type of general guideline for determining how much bitcoins should be worth in the future if it follows a certain path from its current price.
Modeling Bitcoin's money supply mathematically, and knowing that there is a finite number of them, makes this whole process much more rational than just thinking about the possibilities in pure subjective terms.
Before going any further I want to say that no one can know with absolute certainty what will happen to bitcoins price in the future, but using mathematics gives us an idea of where things are headed.
The results presented here are based on very reasonable assumptions for how bitcoin might continue to grow (and then level out) once there are over 21 million bitcoins in existence.
The model shows that bitcoin's price can never go down to zero (thus creating the "death spiral" phenomenon), and as such, bitcoin has an extremely high probability of becoming stable as it approaches infinity.
Conversely, this model also shows that at some point there is a high probability that bitcoin will not continue to grow exponentially forever.
Credit goes to Quantadelic for the awesome original script.
ARUDD
Cari dalam skrip untuk "bitcoin"
Bitcoin Monthly Seasonality [Alpha Extract]The Bitcoin Monthly Seasonality indicator analyzes historical Bitcoin price performance across different months of the year, enabling traders to identify seasonal patterns and potential trading opportunities. This tool helps traders:
Visualize which months historically perform best and worst for Bitcoin.
Track average returns and win rates for each month of the year.
Identify seasonal patterns to enhance trading strategies.
Compare cumulative or individual monthly performance.
🔶 CALCULATION
The indicator processes historical Bitcoin price data to calculate monthly performance metrics
Monthly Return Calculation
Inputs:
Monthly open and close prices.
User-defined lookback period (1-15 years).
Return Types:
Percentage: (monthEndPrice / monthStartPrice - 1) × 100
Price: monthEndPrice - monthStartPrice
Statistical Measures
Monthly Averages: ◦ Average return for each month calculated from historical data.
Win Rate: ◦ Percentage of positive returns for each month.
Best/Worst Detection: ◦ Identifies months with highest and lowest average returns.
Cumulative Option
Standard View: Shows discrete monthly performance.
Cumulative View: Shows compounding effect of consecutive months.
Example Calculation (Pine Script):
monthReturn = returnType == "Percentage" ?
(monthEndPrice / monthStartPrice - 1) * 100 :
monthEndPrice - monthStartPrice
calcWinRate(arr) =>
winCount = 0
totalCount = array.size(arr)
if totalCount > 0
for i = 0 to totalCount - 1
if array.get(arr, i) > 0
winCount += 1
(winCount / totalCount) * 100
else
0.0
🔶 DETAILS
Visual Features
Monthly Performance Bars: ◦ Color-coded bars (teal for positive, red for negative returns). ◦ Special highlighting for best (yellow) and worst (fuchsia) months.
Optional Trend Line: ◦ Shows continuous performance across months.
Monthly Axis Labels: ◦ Clear month names for easy reference.
Statistics Table: ◦ Comprehensive view of monthly performance metrics. ◦ Color-coded rows based on performance.
Interpretation
Strong Positive Months: Historically bullish periods for Bitcoin.
Strong Negative Months: Historically bearish periods for Bitcoin.
Win Rate Analysis: Higher win rates indicate more consistently positive months.
Pattern Recognition: Identify recurring seasonal patterns across years.
Best/Worst Identification: Quickly spot the historically strongest and weakest months.
🔶 EXAMPLES
The indicator helps identify key seasonal patterns
Bullish Seasons: Visualize historically strong months where Bitcoin tends to perform well, allowing traders to align long positions with favorable seasonality.
Bearish Seasons: Identify historically weak months where Bitcoin tends to underperform, helping traders avoid unfavorable periods or consider short positions.
Seasonal Strategy Development: Create trading strategies that capitalize on recurring monthly patterns, such as entering positions in historically strong months and reducing exposure during weak months.
Year-to-Year Comparison: Assess how current year performance compares to historical seasonal patterns to identify anomalies or confirmation of trends.
🔶 SETTINGS
Customization Options
Lookback Period: Adjust the number of years (1-15) used for historical analysis.
Return Type: Choose between percentage returns or absolute price changes.
Cumulative Option: Toggle between discrete monthly performance or cumulative effect.
Visual Style Options: Bar Display: Enable/disable and customize colors for positive/negative bars, Line Display: Enable/disable and customize colors for trend line, Axes Display: Show/hide reference axes.
Visual Enhancement: Best/Worst Month Highlighting: Toggle special highlighting of extreme months, Custom highlight colors for best and worst performing months.
The Bitcoin Monthly Seasonality indicator provides traders with valuable insights into Bitcoin's historical performance patterns throughout the year, helping to identify potentially favorable and unfavorable trading periods based on seasonal tendencies.
Bitcoin Fundamentals - Bitcoin Block RewardThe Bitcoin Block Reward is the batch of new Bitcoins generated by the miners after solving each block.
The Block Reward is set as a basic rule and cannot be changed without agreement between the entire Bitcoin network. It started at 50 BTC during the first period. Afterwards the Block Reward gets adjusted to half of it value (Halving Event) on each cycle of 210000 blocks mined.
This is the only way that new bitcoins are created. It creates an incentive for miners to secure the network.
Over time the Block Reward will decreases to a value that might not cover the mining costs. At that point, the use of the Bitcoin Network might have increased sufficiently as to generate enough transaction fees to cover the mining costs.
MOTIVATION
Even though this is a very simple indicator, I'm currently missing a data source to compute the Block Reward value within Tradingview. Therefore, I created this indicator and its associated library function to enable its visualization and (eventually) for coders to make use of the source function to power more elaborate scripts related to the Halving Events.
Hope that helps!
Bitcoin Power Law Bands (BTC Power Law) Indicator█ OVERVIEW
The 'Bitcoin Power Law Bands' indicator is a set of three US dollar price trendlines and two price bands for bitcoin , indicating overall long-term trend, support and resistance levels as well as oversold and overbought conditions. The magnitude and growth of the middle (Center) line is determined by double logarithmic (log-log) regression on the entire USD price history of bitcoin . The upper (Resistance) and lower (Support) lines follow the same trajectory but multiplied by respective (fixed) factors. These two lines indicate levels where the price of bitcoin is expected to meet strong long-term resistance or receive strong long-term support. The two bands between the three lines are price levels where bitcoin may be considered overbought or oversold.
All parameters and visuals may be customized by the user as needed.
█ CONCEPTS
Long-term models
Long-term price models have many challenges, the most significant of which is getting the growth curve right overall. No one can predict how a certain market, asset class, or financial instrument will unfold over several decades. In the case of bitcoin , price history is very limited and extremely volatile, and this further complicates the situation. Fortunately for us, a few smart people already had some bright ideas that seem to have stood the test of time.
Power law
The so-called power law is the only long-term bitcoin price model that has a chance of survival for the years ahead. The idea behind the power law is very simple: over time, the rapid (exponential) initial growth cannot possibly be sustained (see The seduction of the exponential curve for a fun take on this). Year-on-year returns, therefore, must decrease over time, which leads us to the concept of diminishing returns and the power law. In this context, the power law translates to linear growth on a chart with both its axes scaled logarithmically. This is called the log-log chart (as opposed to the semilog chart you see above, on which only one of the axes - price - is logarithmic).
Log-log regression
When both price and time are scaled logarithmically, the power law leads to a linear relationship between them. This in turn allows us to apply linear regression techniques, which will find the best-fitting straight line to the data points in question. The result of performing this log-log regression (i.e. linear regression on a log-log scaled dataset) is two parameters: slope (m) and intercept (b). These parameters fully describe the relationship between price and time as follows: log(P) = m * log(T) + b, where P is price and T is time. Price is measured in US dollars , and Time is counted as the number of days elapsed since bitcoin 's genesis block.
DPC model
The final piece of our puzzle is the Dynamic Power Cycle (DPC) price model of bitcoin . DPC is a long-term cyclic model that uses the power law as its foundation, to which a periodic component stemming from the block subsidy halving cycle is applied dynamically. The regression parameters of this model are re-calculated daily to ensure longevity. For the 'Bitcoin Power Law Bands' indicator, the slope and intercept parameters were calculated on publication date (March 6, 2022). The slope of the Resistance Line is the same as that of the Center Line; its intercept was determined by fitting the line onto the Nov 2021 cycle peak. The slope of the Support Line is the same as that of the Center Line; its intercept was determined by fitting the line onto the Dec 2018 trough of the previous cycle. Please see the Limitations section below on the implications of a static model.
█ FEATURES
Inputs
• Parameters
• Center Intercept (b) and Slope (m): These log-log regression parameters control the behavior of the grey line in the middle
• Resistance Intercept (b) and Slope (m): These log-log regression parameters control the behavior of the red line at the top
• Support Intercept (b) and Slope (m): These log-log regression parameters control the behavior of the green line at the bottom
• Controls
• Plot Line Fill: N/A
• Plot Opportunity Label: Controls the display of current price level relative to the Center, Resistance and Support Lines
Style
• Visuals
• Center: Control, color, opacity, thickness, price line control and line style of the Center Line
• Resistance: Control, color, opacity, thickness, price line control and line style of the Resistance Line
• Support: Control, color, opacity, thickness, price line control and line style of the Support Line
• Plots Background: Control, color and opacity of the Upper Band
• Plots Background: Control, color and opacity of the Lower Band
• Labels: N/A
• Output
• Labels on price scale: Controls the display of current Center, Resistance and Support Line values on the price scale
• Values in status line: Controls the display of current Center, Resistance and Support Line values in the indicator's status line
█ HOW TO USE
The indicator includes three price lines:
• The grey Center Line in the middle shows the overall long-term bitcoin USD price trend
• The red Resistance Line at the top is an indication of where the bitcoin USD price is expected to meet strong long-term resistance
• The green Support Line at the bottom is an indication of where the bitcoin USD price is expected to receive strong long-term support
These lines envelope two price bands:
• The red Upper Band between the Center and Resistance Lines is an area where bitcoin is considered overbought (i.e. too expensive)
• The green Lower Band between the Support and Center Lines is an area where bitcoin is considered oversold (i.e. too cheap)
The power law model assumes that the price of bitcoin will fluctuate around the Center Line, by meeting resistance at the Resistance Line and finding support at the Support Line. When the current price is well below the Center Line (i.e. well into the green Lower Band), bitcoin is considered too cheap (oversold). When the current price is well above the Center Line (i.e. well into the red Upper Band), bitcoin is considered too expensive (overbought). This idea alone is not sufficient for profitable trading, but, when combined with other factors, it could guide the user's decision-making process in the right direction.
█ LIMITATIONS
The indicator is based on a static model, and for this reason it will gradually lose its usefulness. The Center Line is the most durable of the three lines since the long-term growth trend of bitcoin seems to deviate little from the power law. However, how far price extends above and below this line will change with every halving cycle (as can be seen for past cycles). Periodic updates will be needed to keep the indicator relevant. The user is invited to adjust the slope and intercept parameters manually between two updates of the indicator.
█ RAMBLINGS
The 'Bitcoin Power Law Bands' indicator is a useful tool for users wishing to place bitcoin in a macro context. As described above, the price level relative to the three lines is a rough indication of whether bitcoin is over- or undervalued. Users wishing to gain more insight into bitcoin price trends may follow the author's periodic updates of the DPC model (contact information below).
█ NOTES
The author regularly posts on Twitter using the @DeFi_initiate handle.
█ THANKS
Many thanks to the following individuals, who - one way or another - made the 'Bitcoin Power Law Bands' indicator possible:
• TradingView user 'capriole_charles', whose open-source 'Bitcoin Power Law Corridor' script was the basis for this indicator
• Harold Christopher Burger, whose Bitcoin’s natural long-term power-law corridor of growth article (2019) was the basis for the 'Bitcoin Power Law Corridor' script
• Bitcoin Forum user "Trololo", who posted the original power law model at Logarithmic (non-linear) regression - Bitcoin estimated value (2014)
Bitcoin Comparison to GBTC!This script tells you if GBTC is overvalued or undervalued compared to Bitcoin.
Bitcoin Price User Correlation [aamonkey]You can only use this for BTC.
Bitcoin over time tends to be priced at 7000 times the number of users (in terms of market cap).
Calculation:
Number of Wallets*7000/(Circulating Supply or 21,000,000)
Settings:
You can decide whether you want to use the Circulating Supply or 21,000,000 as a reference.
The default settings are using 21,000,000 because it seems to be more accurate.
You can easily switch between both versions by checking the box in the settings.
Interesting Findings:
Using circulating supply:
- Most of the time we are under the estimated ("PUC") line
- Once we break above the PUC line we are in the parabolic phase of the Bullrun
- In history, we broke only 4 times above the PUC
- Once we are above the PUC we see crazy growth (parabolic phase)
- We don't spend much time above the PUC
- From breaking the PUC to the new All-Time High of the cycle we took in order: 3 Days, 7 Days, 22 Days, 30 Days
- So the trend is increasing (We are taking more and more time until we see the ATH)
- Currently, we are about to break the PUC
- Then I expect the parabolic phase to begin
- I expect the run to last about 30 days
Bitcoin Expectile Model [LuxAlgo]The Bitcoin Expectile Model is a novel approach to forecasting Bitcoin, inspired by the popular Bitcoin Quantile Model by PlanC. By fitting multiple Expectile regressions to the price, we highlight zones of corrections or accumulations throughout the Bitcoin price evolution.
While we strongly recommend using this model with the Bitcoin All Time History Index INDEX:BTCUSD on the 3 days or weekly timeframe using a logarithmic scale, this model can be applied to any asset using the daily timeframe or superior.
Please note that here on TradingView, this model was solely designed to be used on the Bitcoin 1W chart, however, it can be experimented on other assets or timeframes if of interest.
🔶 USAGE
The Bitcoin Expectile Model can be applied similarly to models used for Bitcoin, highlighting lower areas of possible accumulation (support) and higher areas that allow for the anticipation of potential corrections (resistance).
By default, this model fits 7 individual Expectiles Log-Log Regressions to the price, each with their respective expectile ( tau ) values (here multiplied by 100 for the user's convenience). Higher tau values will return a fit closer to the higher highs made by the price of the asset, while lower ones will return fits closer to the lower prices observed over time.
Each zone is color-coded and has a specific interpretation. The green zone is a buy zone for long-term investing, purple is an anomaly zone for market bottoms that over-extend, while red is considered the distribution zone.
The fits can be extrapolated, helping to chart a course for the possible evolution of Bitcoin prices. Users can select the end of the forecast as a date using the "Forecast End" setting.
While the model is made for Bitcoin using a log scale, other assets showing a tendency to have a trend evolving in a single direction can be used. See the chart above on QQQ weekly using a linear scale as an example.
The Start Date can also allow fitting the model more locally, rather than over a large range of prices. This can be useful to identify potential shorter-term support/resistance areas.
🔶 DETAILS
🔹 On Quantile and Expectile Regressions
Quantile and Expectile regressions are similar; both return extremities that can be used to locate and predict prices where tops/bottoms could be more likely to occur.
The main difference lies in what we are trying to minimize, which, for Quantile regression, is commonly known as Quantile loss (or pinball loss), and for Expectile regression, simply Expectile loss.
You may refer to external material to go more in-depth about these loss functions; however, while they are similar and involve weighting specific prices more than others relative to our parameter tau, Quantile regression involves minimizing a weighted mean absolute error, while Expectile regression minimizes a weighted squared error.
The squared error here allows us to compute Expectile regression more easily compared to Quantile regression, using Iteratively reweighted least squares. For Quantile regression, a more elaborate method is needed.
In terms of comparison, Quantile regression is more robust, and easier to interpret, with quantiles being related to specific probabilities involving the underlying cumulative distribution function of the dataset; on the other expectiles are harder to interpret.
🔹 Trimming & Alterations
It is common to observe certain models ignoring very early Bitcoin price ranges. By default, we start our fit at the date 2010-07-16 to align with existing models.
By default, the model uses the number of time units (days, weeks...etc) elapsed since the beginning of history + 1 (to avoid NaN with log) as independent variable, however the Bitcoin All Time History Index INDEX:BTCUSD do not include the genesis block, as such users can correct for this by enabling the "Correct for Genesis block" setting, which will add the amount of missed bars from the Genesis block to the start oh the chart history.
🔶 SETTINGS
Start Date: Starting interval of the dataset used for the fit.
Correct for genesis block: When enabled, offset the X axis by the number of bars between the Bitcoin genesis block time and the chart starting time.
🔹 Expectiles
Toggle: Enable fit for the specified expectile. Disabling one fit will make the script faster to compute.
Expectile: Expectile (tau) value multiplied by 100 used for the fit. Higher values will produce fits that are located near price tops.
🔹 Forecast
Forecast End: Time at which the forecast stops.
🔹 Model Fit
Iterations Number: Number of iterations performed during the reweighted least squares process, with lower values leading to less accurate fits, while higher values will take more time to compute.
Bitcoin Power Law [LuxAlgo]The Bitcoin Power Law tool is a representation of Bitcoin prices first proposed by Giovanni Santostasi, Ph.D. It plots BTCUSD daily closes on a log10-log10 scale, and fits a linear regression channel to the data.
This channel helps traders visualise when the price is historically in a zone prone to tops or located within a discounted zone subject to future growth.
🔶 USAGE
Giovanni Santostasi, Ph.D. originated the Bitcoin Power-Law Theory; this implementation places it directly on a TradingView chart. The white line shows the daily closing price, while the cyan line is the best-fit regression.
A channel is constructed from the linear fit root mean squared error (RMSE), we can observe how price has repeatedly oscillated between each channel areas through every bull-bear cycle.
Excursions into the upper channel area can be followed by price surges and finishing on a top, whereas price touching the lower channel area coincides with a cycle low.
Users can change the channel areas multipliers, helping capture moves more precisely depending on the intended usage.
This tool only works on the daily BTCUSD chart. Ticker and timeframe must match exactly for the calculations to remain valid.
🔹 Linear Scale
Users can toggle on a linear scale for the time axis, in order to obtain a higher resolution of the price, (this will affect the linear regression channel fit, making it look poorer).
🔶 DETAILS
One of the advantages of the Power Law Theory proposed by Giovanni Santostasi is its ability to explain multiple behaviors of Bitcoin. We describe some key points below.
🔹 Power-Law Overview
A power law has the form y = A·xⁿ , and Bitcoin’s key variables follow this pattern across many orders of magnitude. Empirically, price rises roughly with t⁶, hash-rate with t¹² and the number of active addresses with t³.
When we plot these on log-log axes they appear as straight lines, revealing a scale-invariant system whose behaviour repeats proportionally as it grows.
🔹 Feedback-Loop Dynamics
Growth begins with new users, whose presence pushes the price higher via a Metcalfe-style square-law. A richer price pool funds more mining hardware; the Difficulty Adjustment immediately raises the hash-rate requirement, keeping profit margins razor-thin.
A higher hash rate secures the network, which in turn attracts the next wave of users. Because risk and Difficulty act as braking forces, user adoption advances as a power of three in time rather than an unchecked S-curve. This circular causality repeats without end, producing the familiar boom-and-bust cadence around the long-term power-law channel.
🔹 Scale Invariance & Predictions
Scale invariance means that enlarging the timeline in log-log space leaves the trajectory unchanged.
The same geometric proportions that described the first dollar of value can therefore extend to a projected million-dollar bitcoin, provided no catastrophic break occurs. Institutional ETF inflows supply fresh capital but do not bend the underlying slope; only a persistent deviation from the line would falsify the current model.
🔹 Implications
The theory assigns scarcity no direct role; iterative feedback and the Difficulty Adjustment are sufficient to govern Bitcoin’s expansion. Long-term valuation should focus on position within the power-law channel, while bubbles—sharp departures above trend that later revert—are expected punctuations of an otherwise steady climb.
Beyond about 2040, disruptive technological shifts could alter the parameters, but for the next order of magnitude the present slope remains the simplest, most robust guide.
Bitcoin behaves less like a traditional asset and more like a self-organising digital organism whose value, security, and adoption co-evolve according to immutable power-law rules.
🔶 SETTINGS
🔹 General
Start Calculation: Determine the start date used by the calculation, with any prior prices being ignored. (default - 15 Jul 2010)
Use Linear Scale for X-Axis: Convert the horizontal axis from log(time) to linear calendar time
🔹 Linear Regression
Show Regression Line: Enable/disable the central power-law trend line
Regression Line Color: Choose the colour of the regression line
Mult 1: Toggle line & fill, set multiplier (default +1), pick line colour and area fill colour
Mult 2: Toggle line & fill, set multiplier (default +0.5), pick line colour and area fill colour
Mult 3: Toggle line & fill, set multiplier (default -0.5), pick line colour and area fill colour
Mult 4: Toggle line & fill, set multiplier (default -1), pick line colour and area fill colour
🔹 Style
Price Line Color: Select the colour of the BTC price plot
Auto Color: Automatically choose the best contrast colour for the price line
Price Line Width: Set the thickness of the price line (1 – 5 px)
Show Halvings: Enable/disable dotted vertical lines at each Bitcoin halving
Halvings Color: Choose the colour of the halving lines
Bitcoin Polynomial Regression ModelThis is the main version of the script. Click here for the Oscillator part of the script.
💡Why this model was created:
One of the key issues with most existing models, including our own Bitcoin Log Growth Curve Model , is that they often fail to realistically account for diminishing returns. As a result, they may present overly optimistic bull cycle targets (hence, we introduced alternative settings in our previous Bitcoin Log Growth Curve Model).
This new model however, has been built from the ground up with a primary focus on incorporating the principle of diminishing returns. It directly responds to this concept, which has been briefly explored here .
📉The theory of diminishing returns:
This theory suggests that as each four-year market cycle unfolds, volatility gradually decreases, leading to more tempered price movements. It also implies that the price increase from one cycle peak to the next will decrease over time as the asset matures. The same pattern applies to cycle lows and the relationship between tops and bottoms. In essence, these price movements are interconnected and should generally follow a consistent pattern. We believe this model provides a more realistic outlook on bull and bear market cycles.
To better understand this theory, the relationships between cycle tops and bottoms are outlined below:https://www.tradingview.com/x/7Hldzsf2/
🔧Creation of the model:
For those interested in how this model was created, the process is explained here. Otherwise, feel free to skip this section.
This model is based on two separate cubic polynomial regression lines. One for the top price trend and another for the bottom. Both follow the general cubic polynomial function:
ax^3 +bx^2 + cx + d.
In this equation, x represents the weekly bar index minus an offset, while a, b, c, and d are determined through polynomial regression analysis. The input (x, y) values used for the polynomial regression analysis are as follows:
Top regression line (x, y) values:
113, 18.6
240, 1004
451, 19128
655, 65502
Bottom regression line (x, y) values:
103, 2.5
267, 211
471, 3193
676, 16255
The values above correspond to historical Bitcoin cycle tops and bottoms, where x is the weekly bar index and y is the weekly closing price of Bitcoin. The best fit is determined using metrics such as R-squared values, residual error analysis, and visual inspection. While the exact details of this evaluation are beyond the scope of this post, the following optimal parameters were found:
Top regression line parameter values:
a: 0.000202798
b: 0.0872922
c: -30.88805
d: 1827.14113
Bottom regression line parameter values:
a: 0.000138314
b: -0.0768236
c: 13.90555
d: -765.8892
📊Polynomial Regression Oscillator:
This publication also includes the oscillator version of the this model which is displayed at the bottom of the screen. The oscillator applies a logarithmic transformation to the price and the regression lines using the formula log10(x) .
The log-transformed price is then normalized using min-max normalization relative to the log-transformed top and bottom regression line with the formula:
normalized price = log(close) - log(bottom regression line) / log(top regression line) - log(bottom regression line)
This transformation results in a price value between 0 and 1 between both the regression lines. The Oscillator version can be found here.
🔍Interpretation of the Model:
In general, the red area represents a caution zone, as historically, the price has often been near its cycle market top within this range. On the other hand, the green area is considered an area of opportunity, as historically, it has corresponded to the market bottom.
The top regression line serves as a signal for the absolute market cycle peak, while the bottom regression line indicates the absolute market cycle bottom.
Additionally, this model provides a predicted range for Bitcoin's future price movements, which can be used to make extrapolated predictions. We will explore this further below.
🔮Future Predictions:
Finally, let's discuss what this model actually predicts for the potential upcoming market cycle top and the corresponding market cycle bottom. In our previous post here , a cycle interval analysis was performed to predict a likely time window for the next cycle top and bottom:
In the image, it is predicted that the next top-to-top cycle interval will be 208 weeks, which translates to November 3rd, 2025. It is also predicted that the bottom-to-top cycle interval will be 152 weeks, which corresponds to October 13th, 2025. On the macro level, these two dates align quite well. For our prediction, we take the average of these two dates: October 24th 2025. This will be our target date for the bull cycle top.
Now, let's do the same for the upcoming cycle bottom. The bottom-to-bottom cycle interval is predicted to be 205 weeks, which translates to October 19th, 2026, and the top-to-bottom cycle interval is predicted to be 259 weeks, which corresponds to October 26th, 2026. We then take the average of these two dates, predicting a bear cycle bottom date target of October 19th, 2026.
Now that we have our predicted top and bottom cycle date targets, we can simply reference these two dates to our model, giving us the Bitcoin top price prediction in the range of 152,000 in Q4 2025 and a subsequent bottom price prediction in the range of 46,500 in Q4 2026.
For those interested in understanding what this specifically means for the predicted diminishing return top and bottom cycle values, the image below displays these predicted values. The new values are highlighted in yellow:
And of course, keep in mind that these targets are just rough estimates. While we've done our best to estimate these targets through a data-driven approach, markets will always remain unpredictable in nature. What are your targets? Feel free to share them in the comment section below.
Bitcoin Polynomial Regression OscillatorThis is the oscillator version of the script. Click here for the other part of the script.
💡Why this model was created:
One of the key issues with most existing models, including our own Bitcoin Log Growth Curve Model , is that they often fail to realistically account for diminishing returns. As a result, they may present overly optimistic bull cycle targets (hence, we introduced alternative settings in our previous Bitcoin Log Growth Curve Model).
This new model however, has been built from the ground up with a primary focus on incorporating the principle of diminishing returns. It directly responds to this concept, which has been briefly explored here .
📉The theory of diminishing returns:
This theory suggests that as each four-year market cycle unfolds, volatility gradually decreases, leading to more tempered price movements. It also implies that the price increase from one cycle peak to the next will decrease over time as the asset matures. The same pattern applies to cycle lows and the relationship between tops and bottoms. In essence, these price movements are interconnected and should generally follow a consistent pattern. We believe this model provides a more realistic outlook on bull and bear market cycles.
To better understand this theory, the relationships between cycle tops and bottoms are outlined below:https://www.tradingview.com/x/7Hldzsf2/
🔧Creation of the model:
For those interested in how this model was created, the process is explained here. Otherwise, feel free to skip this section.
This model is based on two separate cubic polynomial regression lines. One for the top price trend and another for the bottom. Both follow the general cubic polynomial function:
ax^3 +bx^2 + cx + d.
In this equation, x represents the weekly bar index minus an offset, while a, b, c, and d are determined through polynomial regression analysis. The input (x, y) values used for the polynomial regression analysis are as follows:
Top regression line (x, y) values:
113, 18.6
240, 1004
451, 19128
655, 65502
Bottom regression line (x, y) values:
103, 2.5
267, 211
471, 3193
676, 16255
The values above correspond to historical Bitcoin cycle tops and bottoms, where x is the weekly bar index and y is the weekly closing price of Bitcoin. The best fit is determined using metrics such as R-squared values, residual error analysis, and visual inspection. While the exact details of this evaluation are beyond the scope of this post, the following optimal parameters were found:
Top regression line parameter values:
a: 0.000202798
b: 0.0872922
c: -30.88805
d: 1827.14113
Bottom regression line parameter values:
a: 0.000138314
b: -0.0768236
c: 13.90555
d: -765.8892
📊Polynomial Regression Oscillator:
This publication also includes the oscillator version of the this model which is displayed at the bottom of the screen. The oscillator applies a logarithmic transformation to the price and the regression lines using the formula log10(x) .
The log-transformed price is then normalized using min-max normalization relative to the log-transformed top and bottom regression line with the formula:
normalized price = log(close) - log(bottom regression line) / log(top regression line) - log(bottom regression line)
This transformation results in a price value between 0 and 1 between both the regression lines.
🔍Interpretation of the Model:
In general, the red area represents a caution zone, as historically, the price has often been near its cycle market top within this range. On the other hand, the green area is considered an area of opportunity, as historically, it has corresponded to the market bottom.
The top regression line serves as a signal for the absolute market cycle peak, while the bottom regression line indicates the absolute market cycle bottom.
Additionally, this model provides a predicted range for Bitcoin's future price movements, which can be used to make extrapolated predictions. We will explore this further below.
🔮Future Predictions:
Finally, let's discuss what this model actually predicts for the potential upcoming market cycle top and the corresponding market cycle bottom. In our previous post here , a cycle interval analysis was performed to predict a likely time window for the next cycle top and bottom:
In the image, it is predicted that the next top-to-top cycle interval will be 208 weeks, which translates to November 3rd, 2025. It is also predicted that the bottom-to-top cycle interval will be 152 weeks, which corresponds to October 13th, 2025. On the macro level, these two dates align quite well. For our prediction, we take the average of these two dates: October 24th 2025. This will be our target date for the bull cycle top.
Now, let's do the same for the upcoming cycle bottom. The bottom-to-bottom cycle interval is predicted to be 205 weeks, which translates to October 19th, 2026, and the top-to-bottom cycle interval is predicted to be 259 weeks, which corresponds to October 26th, 2026. We then take the average of these two dates, predicting a bear cycle bottom date target of October 19th, 2026.
Now that we have our predicted top and bottom cycle date targets, we can simply reference these two dates to our model, giving us the Bitcoin top price prediction in the range of 152,000 in Q4 2025 and a subsequent bottom price prediction in the range of 46,500 in Q4 2026.
For those interested in understanding what this specifically means for the predicted diminishing return top and bottom cycle values, the image below displays these predicted values. The new values are highlighted in yellow:
And of course, keep in mind that these targets are just rough estimates. While we've done our best to estimate these targets through a data-driven approach, markets will always remain unpredictable in nature. What are your targets? Feel free to share them in the comment section below.
Bitcoin Bubble Risk (Adjusted for Diminishing Returns)Description:
This indicator offers a unique lens through which traders can assess risk in the Bitcoin market, specifically tailored to recognize the phenomenon of diminishing returns. By calculating the natural logarithm of the price relative to a 20-month Simple Moving Average (SMA) and applying a dynamic normalization process, this tool highlights periods of varying risk based on historical price movements and adjusted returns. The indicator is designed to provide nuanced insights into potential risk levels, aiding traders in their decision-making processes.
Usage:
To effectively use this indicator, apply it to your chart while ensuring that Bitcoin's price is set to display in monthly candles. This setting is vital for the indicator to accurately reflect the market's risk levels, as it relies on long-term data aggregation to inform its analysis.
This tool is especially beneficial for traders focused on medium to long-term investment horizons in Bitcoin, offering insights into when the market may be entering higher or lower risk phases. By incorporating this indicator into your analysis, you can gain a deeper understanding of potential risk exposures based on the adjusted price trends and market conditions.
Originality and Utility:
This script stands out for its innovative approach to risk analysis in the cryptocurrency space. By adjusting for the diminishing returns seen in mature markets, it provides a refined perspective on risk levels, enhancing traditional methodologies. This script is a significant contribution to the TradingView community, offering a unique tool for traders aiming to navigate the complexities of the Bitcoin market with informed risk management strategies.
Important Note:
This indicator is for informational purposes only and should not be considered investment advice. Users are encouraged to conduct their own research and consult with financial professionals before making investment decisions. The accuracy of the indicator's predictions can only be ensured when applied to monthly candlestick charts of Bitcoin.
Bitcoin Leverage Sentiment - Strategy [presentTrading]█ Introduction and How it is Different
The "Bitcoin Leverage Sentiment - Strategy " represents a novel approach in the realm of cryptocurrency trading by focusing on sentiment analysis through leveraged positions in Bitcoin. Unlike traditional strategies that primarily rely on price action or technical indicators, this strategy leverages the power of Z-Score analysis to gauge market sentiment by examining the ratio of leveraged long to short positions. By assessing how far the current sentiment deviates from the historical norm, it provides a unique lens to spot potential reversals or continuation in market trends, making it an innovative tool for traders who wish to incorporate market psychology into their trading arsenal.
BTC 4h L/S Performance
local
█ Strategy, How It Works: Detailed Explanation
🔶 Data Collection and Ratio Calculation
Firstly, the strategy acquires data on leveraged long (**`priceLongs`**) and short positions (**`priceShorts`**) for Bitcoin. The primary metric of interest is the ratio of long positions relative to the total of both long and short positions:
BTC Ratio=priceLongs / (priceLongs+priceShorts)
This ratio reflects the prevailing market sentiment, where values closer to 1 indicate a bullish sentiment (dominance of long positions), and values closer to 0 suggest bearish sentiment (prevalence of short positions).
🔶 Z-Score Calculation
The Z-Score is then calculated to standardize the BTC Ratio, allowing for comparison across different time periods. The Z-Score formula is:
Z = (X - μ) / σ
Where:
- X is the current BTC Ratio.
- μ is the mean of the BTC Ratio over a specified period (**`zScoreCalculationPeriod`**).
- σ is the standard deviation of the BTC Ratio over the same period.
The Z-Score helps quantify how far the current sentiment deviates from the historical norm, with high positive values indicating extreme bullish sentiment and high negative values signaling extreme bearish sentiment.
🔶 Signal Generation: Trading signals are derived from the Z-Score as follows:
Long Entry Signal: Occurs when the BTC Ratio Z-Score crosses above the thresholdLongEntry, suggesting bullish sentiment.
- Condition for Long Entry = BTC Ratio Z-Score > thresholdLongEntry
Long Exit/Short Entry Signal: Triggered when the BTC Ratio Z-Score drops below thresholdLongExit for exiting longs or below thresholdShortEntry for entering shorts, indicating a shift to bearish sentiment.
- Condition for Long Exit/Short Entry = BTC Ratio Z-Score < thresholdLongExit or BTC Ratio Z-Score < thresholdShortEntry
Short Exit Signal: Happens when the BTC Ratio Z-Score exceeds the thresholdShortExit, hinting at reducing bearish sentiment and a potential switch to bullish conditions.
- Condition for Short Exit = BTC Ratio Z-Score > thresholdShortExit
🔶Implementation and Visualization: The strategy applies these conditions for trade management, aligning with the selected trade direction. It visualizes the BTC Ratio Z-Score with horizontal lines at entry and exit thresholds, illustrating the current sentiment against historical norms.
█ Trade Direction
The strategy offers flexibility in trade direction, allowing users to choose between long, short, or both, depending on their market outlook and risk tolerance. This adaptability ensures that traders can align the strategy with their individual trading style and market conditions.
█ Usage
To employ this strategy effectively:
1. Customization: Begin by setting the trade direction and adjusting the Z-Score calculation period and entry/exit thresholds to match your trading preferences.
2. Observation: Monitor the Z-Score and its moving average for potential trading signals. Look for crossover events relative to the predefined thresholds to identify entry and exit points.
3. Confirmation: Consider using additional analysis or indicators for signal confirmation, ensuring a comprehensive approach to decision-making.
█ Default Settings
- Trade Direction: Determines if the strategy engages in long, short, or both types of trades, impacting its adaptability to market conditions.
- Timeframe Input: Influences signal frequency and sensitivity, affecting the strategy's responsiveness to market dynamics.
- Z-Score Calculation Period: Affects the strategy’s sensitivity to market changes, with longer periods smoothing data and shorter periods increasing responsiveness.
- Entry and Exit Thresholds: Set the Z-Score levels for initiating or exiting trades, balancing between capturing opportunities and minimizing false signals.
- Impact of Default Settings: Provides a balanced approach to leverage sentiment trading, with adjustments needed to optimize performance across various market conditions.
Bitcoin to GOLD [presentTrading]**Introduction and How it is Different**
Unlike traditional indicators, the BTGR offers a unique perspective on market sentiment and asset valuation by juxtaposing two seemingly disparate assets: Bitcoin, the digital gold, and Gold, the traditional store of value. This article introduces an advanced version of this ratio, complete with upper and lower bands calculated using standard deviations. These bands add an extra layer of analytical depth, allowing for more nuanced trading strategies.
BTCUSD 12h bigger picture
**Economic Principles**
The BTGR is rooted in the economic principles of asset valuation and market sentiment. Gold has long been considered a safe haven asset, a place where investors park their money during times of economic uncertainty. Bitcoin, on the other hand, is often viewed as a high-risk, high-reward investment. By comparing the two, the BTGR provides insights into the broader market sentiment.
- Risk Appetite: A high BTGR indicates a bullish sentiment towards riskier assets like Bitcoin.
- Market Uncertainty: A low BTGR suggests a bearish sentiment and a flight to the safety of Gold.
- Asset Diversification: The BTGR can be used as a tool for portfolio diversification, helping investors balance risk and reward.
**How to Use It**
Setting Up the Indicator
- Platform: The indicator is designed for use on TradingView.
- Time Frame: A 480-minute time frame is recommended for more accurate signals.
- Parameters: The moving average is set at 200 periods, and the standard deviation is calculated over the same period.
**Trading Signal**
Long Entry: Consider going long when the BTGR crosses above the upper band.
Short Entry: Consider going short when the BTGR crosses below the lower band.
Note: Due to the issue that the number of trading is less than about 100 times, the corresponding strategy is not allowed to publish.
Bitcoin Support BandsSMA and EMA support/resistance bands for Bitcoin. Based on 4 week multiples; 1 month, 3 month, 6 month, 1 year, 2 year, 4 year.
Bitcoin Difficult Model [ChuckBanger]Simple script that graphically represents the mining difficulty of Bitcoin. It is ment to be used as a tool to decide when it is good time to dollar cost average (DCA) in your Bitcoin hodl position. When Price is below the difficulty model it is usually a good time to DCA.
Formula for the model used in this calculation is 0.002 * difficulty ^ 0.51. It is possible to change this numbers if necessarily.
Bitcoin Logarithmic Growth CurvesThis plots logarithmic curves fitted to major Bitcoin bear market tops & bottoms. Top line is fitted to bull tops, bottom line is fitted to lower areas of the logarithmic price trend (which is not always the same as bear market bottoms). Middle line is the median of the top & bottom, and the faded solid lines are fibonacci levels in between.
Inspired by & based on a Medium post by Harold Christopher Burger, which shows how linear Bitcoin's long-term price growth is when plotted on a double-log chart (log scaling on the price AND time axis).
These curves will only make sense for tickers representing Bitcoin vs. USD (such as BITSTAMP:BTCUSD, BITMEX:XBTUSD, BLX index). Plotting on other assets will probably end up with lines that shoot off into space without any relationship to the underlying price action.
The upper, middle & lower curves can be projected into the future, which can be turned on or off in the indicator settings. The fibonacci levels can also be switched on/off. And the upper & lower curve intercepts & slopes can be tweaked.
I'm releasing this open-source, if you end up making something cool based off of this code, I don't need attribution but please hit me up on here or on twitter (same username) so I can check out what ya made. Thanks, hope y'all enjoy it.
Bitcoin Power Law Clock [LuxAlgo]The Bitcoin Power Law Clock is a unique representation of Bitcoin prices proposed by famous Bitcoin analyst and modeler Giovanni Santostasi.
It displays a clock-like figure with the Bitcoin price and average lines as spirals, as well as the 12, 3, 6, and 9 hour marks as key points in the cycle.
🔶 USAGE
Giovanni Santostasi, Ph.D., is the creator and discoverer of the Bitcoin Power Law Theory. He is passionate about Bitcoin and has 12 years of experience analyzing it and creating price models.
As we can see in the above chart, the tool is super intuitive. It displays a clock-like figure with the current Bitcoin price at 10:20 on a 12-hour scale.
This tool only works on the 1D INDEX:BTCUSD chart. The ticker and timeframe must be exact to ensure proper functionality.
According to the Bitcoin Power Law Theory, the key cycle points are marked at the extremes of the clock: 12, 3, 6, and 9 hours. According to the theory, the current Bitcoin prices are in a frenzied bull market on their way to the top of the cycle.
🔹 Enable/Disable Elements
All of the elements on the clock can be disabled. If you disable them all, only an empty space will remain.
The different charts above show various combinations. Traders can customize the tool to their needs.
🔹 Auto scale
The clock has an auto-scale feature that is enabled by default. Traders can adjust the size of the clock by disabling this feature and setting the size in the settings panel.
The image above shows different configurations of this feature.
🔶 SETTINGS
🔹 Price
Price: Enable/disable price spiral, select color, and enable/disable curved mode
Average: Enable/disable average spiral, select color, and enable/disable curved mode
🔹 Style
Auto scale: Enable/disable automatic scaling or set manual fixed scaling for the spirals
Lines width: Width of each spiral line
Text Size: Select text size for date tags and price scales
Prices: Enable/disable price scales on the x-axis
Handle: Enable/disable clock handle
Halvings: Enable/disable Halvings
Hours: Enable/disable hours and key cycle points
🔹 Time & Price Dashboard
Show Time & Price: Enable/disable time & price dashboard
Location: Dashboard location
Size: Dashboard size
Bitcoin Power Law OscillatorThis is the oscillator version of the script. The main body of the script can be found here.
Understanding the Bitcoin Power Law Model
Also called the Long-Term Bitcoin Power Law Model. The Bitcoin Power Law model tries to capture and predict Bitcoin's price growth over time. It assumes that Bitcoin's price follows an exponential growth pattern, where the price increases over time according to a mathematical relationship.
By fitting a power law to historical data, the model creates a trend line that represents this growth. It then generates additional parallel lines (support and resistance lines) to show potential price boundaries, helping to visualize where Bitcoin’s price could move within certain ranges.
In simple terms, the model helps us understand Bitcoin's general growth trajectory and provides a framework to visualize how its price could behave over the long term.
The Bitcoin Power Law has the following function:
Power Law = 10^(a + b * log10(d))
Consisting of the following parameters:
a: Power Law Intercept (default: -17.668).
b: Power Law Slope (default: 5.926).
d: Number of days since a reference point(calculated by counting bars from the reference point with an offset).
Explanation of the a and b parameters:
Roughly explained, the optimal values for the a and b parameters are determined through a process of linear regression on a log-log scale (after applying a logarithmic transformation to both the x and y axes). On this log-log scale, the power law relationship becomes linear, making it possible to apply linear regression. The best fit for the regression is then evaluated using metrics like the R-squared value, residual error analysis, and visual inspection. This process can be quite complex and is beyond the scope of this post.
Applying vertical shifts to generate the other lines:
Once the initial power-law is created, additional lines are generated by applying a vertical shift. This shift is achieved by adding a specific number of days (or years in case of this script) to the d-parameter. This creates new lines perfectly parallel to the initial power law with an added vertical shift, maintaining the same slope and intercept.
In the case of this script, shifts are made by adding +365 days, +2 * 365 days, +3 * 365 days, +4 * 365 days, and +5 * 365 days, effectively introducing one to five years of shifts. This results in a total of six Power Law lines, as outlined below (From lowest to highest):
Base Power Law Line (no shift)
1-year shifted line
2-year shifted line
3-year shifted line
4-year shifted line
5-year shifted line
The six power law lines:
Bitcoin Power Law Oscillator
This publication also includes the oscillator version of the Bitcoin Power Law. This version applies a logarithmic transformation to the price, Base Power Law Line, and 5-year shifted line using the formula: log10(x) .
The log-transformed price is then normalized using min-max normalization relative to the log-transformed Base Power Law Line and 5-year shifted line with the formula:
normalized price = log(close) - log(Base Power Law Line) / log(5-year shifted line) - log(Base Power Law Line)
Finally, the normalized price was multiplied by 5 to map its value between 0 and 5, aligning with the shifted lines.
Interpretation of the Bitcoin Power Law Model:
The shifted Power Law lines provide a framework for predicting Bitcoin's future price movements based on historical trends. These lines are created by applying a vertical shift to the initial Power Law line, with each shifted line representing a future time frame (e.g., 1 year, 2 years, 3 years, etc.).
By analyzing these shifted lines, users can make predictions about minimum price levels at specific future dates. For example, the 5-year shifted line will act as the main support level for Bitcoin’s price in 5 years, meaning that Bitcoin’s price should not fall below this line, ensuring that Bitcoin will be valued at least at this level by that time. Similarly, the 2-year shifted line will serve as the support line for Bitcoin's price in 2 years, establishing that the price should not drop below this line within that time frame.
On the other hand, the 5-year shifted line also functions as an absolute resistance , meaning Bitcoin's price will not exceed this line prior to the 5-year mark. This provides a prediction that Bitcoin cannot reach certain price levels before a specific date. For example, the price of Bitcoin is unlikely to reach $100,000 before 2021, and it will not exceed this price before the 5-year shifted line becomes relevant. After 2028, however, the price is predicted to never fall below $100,000, thanks to the support established by the shifted lines.
In essence, the shifted Power Law lines offer a way to predict both the minimum price levels that Bitcoin will hit by certain dates and the earliest dates by which certain price points will be reached. These lines help frame Bitcoin's potential future price range, offering insight into long-term price behavior and providing a guide for investors and analysts. Lets examine some examples:
Example 1:
In Example 1 it can be seen that point A on the 5-year shifted line acts as major resistance . Also it can be seen that 5 years later this price level now corresponds to the Base Power Law Line and acts as a major support at point B(Note: Vertical yearly grid lines have been added for this purpose👍).
Example 2:
In Example 2, the price level at point C on the 3-year shifted line becomes a major support three years later at point D, now aligning with the Base Power Law Line.
Finally, let's explore some future price predictions, as this script provides projections on the weekly timeframe :
Example 3:
In Example 3, the Bitcoin Power Law indicates that Bitcoin's price cannot surpass approximately $808K before 2030 as can be seen at point E, while also ensuring it will be at least $224K by then (point F).
Bitcoin Power LawThis is the main body version of the script. The Oscillator version can be found here.
Understanding the Bitcoin Power Law Model
Also called the Long-Term Bitcoin Power Law Model. The Bitcoin Power Law model tries to capture and predict Bitcoin's price growth over time. It assumes that Bitcoin's price follows an exponential growth pattern, where the price increases over time according to a mathematical relationship.
By fitting a power law to historical data, the model creates a trend line that represents this growth. It then generates additional parallel lines (support and resistance lines) to show potential price boundaries, helping to visualize where Bitcoin’s price could move within certain ranges.
In simple terms, the model helps us understand Bitcoin's general growth trajectory and provides a framework to visualize how its price could behave over the long term.
The Bitcoin Power Law has the following function:
Power Law = 10^(a + b * log10(d))
Consisting of the following parameters:
a: Power Law Intercept (default: -17.668).
b: Power Law Slope (default: 5.926).
d: Number of days since a reference point(calculated by counting bars from the reference point with an offset).
Explanation of the a and b parameters:
Roughly explained, the optimal values for the a and b parameters are determined through a process of linear regression on a log-log scale (after applying a logarithmic transformation to both the x and y axes). On this log-log scale, the power law relationship becomes linear, making it possible to apply linear regression. The best fit for the regression is then evaluated using metrics like the R-squared value, residual error analysis, and visual inspection. This process can be quite complex and is beyond the scope of this post.
Applying vertical shifts to generate the other lines:
Once the initial power-law is created, additional lines are generated by applying a vertical shift. This shift is achieved by adding a specific number of days (or years in case of this script) to the d-parameter. This creates new lines perfectly parallel to the initial power law with an added vertical shift, maintaining the same slope and intercept.
In the case of this script, shifts are made by adding +365 days, +2 * 365 days, +3 * 365 days, +4 * 365 days, and +5 * 365 days, effectively introducing one to five years of shifts. This results in a total of six Power Law lines, as outlined below (From lowest to highest):
Base Power Law Line (no shift)
1-year shifted line
2-year shifted line
3-year shifted line
4-year shifted line
5-year shifted line
The six power law lines:
Bitcoin Power Law Oscillator
This publication also includes the oscillator version of the Bitcoin Power Law. This version applies a logarithmic transformation to the price, Base Power Law Line, and 5-year shifted line using the formula: log10(x) .
The log-transformed price is then normalized using min-max normalization relative to the log-transformed Base Power Law Line and 5-year shifted line with the formula:
normalized price = log(close) - log(Base Power Law Line) / log(5-year shifted line) - log(Base Power Law Line)
Finally, the normalized price was multiplied by 5 to map its value between 0 and 5, aligning with the shifted lines.
Interpretation of the Bitcoin Power Law Model:
The shifted Power Law lines provide a framework for predicting Bitcoin's future price movements based on historical trends. These lines are created by applying a vertical shift to the initial Power Law line, with each shifted line representing a future time frame (e.g., 1 year, 2 years, 3 years, etc.).
By analyzing these shifted lines, users can make predictions about minimum price levels at specific future dates. For example, the 5-year shifted line will act as the main support level for Bitcoin’s price in 5 years, meaning that Bitcoin’s price should not fall below this line, ensuring that Bitcoin will be valued at least at this level by that time. Similarly, the 2-year shifted line will serve as the support line for Bitcoin's price in 2 years, establishing that the price should not drop below this line within that time frame.
On the other hand, the 5-year shifted line also functions as an absolute resistance , meaning Bitcoin's price will not exceed this line prior to the 5-year mark. This provides a prediction that Bitcoin cannot reach certain price levels before a specific date. For example, the price of Bitcoin is unlikely to reach $100,000 before 2021, and it will not exceed this price before the 5-year shifted line becomes relevant. After 2028, however, the price is predicted to never fall below $100,000, thanks to the support established by the shifted lines.
In essence, the shifted Power Law lines offer a way to predict both the minimum price levels that Bitcoin will hit by certain dates and the earliest dates by which certain price points will be reached. These lines help frame Bitcoin's potential future price range, offering insight into long-term price behavior and providing a guide for investors and analysts. Lets examine some examples:
Example 1:
In Example 1 it can be seen that point A on the 5-year shifted line acts as major resistance . Also it can be seen that 5 years later this price level now corresponds to the Base Power Law Line and acts as a major support at point B (Note: Vertical yearly grid lines have been added for this purpose👍).
Example 2:
In Example 2, the price level at point C on the 3-year shifted line becomes a major support three years later at point D, now aligning with the Base Power Law Line.
Finally, let's explore some future price predictions, as this script provides projections on the weekly timeframe :
Example 3:
In Example 3, the Bitcoin Power Law indicates that Bitcoin's price cannot surpass approximately $808K before 2030 as can be seen at point E, while also ensuring it will be at least $224K by then (point F).
Bitcoin Log Growth Curve OscillatorThis script presents the oscillator version of the Bitcoin Logarithmic Growth Curve 2024 indicator, offering a new perspective on Bitcoin’s long-term price trajectory.
By transforming the original logarithmic growth curve into an oscillator, this version provides a normalized view of price movements within a fixed range, making it easier to identify overbought and oversold conditions.
For a comprehensive explanation of the mathematical derivation, underlying concepts, and overall development of the Bitcoin Logarithmic Growth Curve, we encourage you to explore our primary script, Bitcoin Logarithmic Growth Curve 2024, available here . This foundational script details the regression-based approach used to model Bitcoin’s long-term price evolution.
Normalization Process
The core principle behind this oscillator lies in the normalization of Bitcoin’s price relative to the upper and lower regression boundaries. By applying Min-Max Normalization, we effectively scale the price into a bounded range, facilitating clearer trend analysis. The normalization follows the formula:
normalized price = (upper regresionline − lower regressionline) / (price − lower regressionline)
This transformation ensures that price movements are always mapped within a fixed range, preventing distortions caused by Bitcoin’s exponential long-term growth. Furthermore, this normalization technique has been applied to each of the confidence interval lines, allowing for a structured and systematic approach to analyzing Bitcoin’s historical and projected price behavior.
By representing the logarithmic growth curve in oscillator form, this indicator helps traders and analysts more effectively gauge Bitcoin’s position within its long-term growth trajectory while identifying potential opportunities based on historical price tendencies.
Bitcoin Events HistoryWith this tool, you can travel back to Bitcoin’s very first price quote and retrace its entire history directly on your chart. Major events are plotted as labels or markers, providing context for how significant moments shaped Bitcoin’s journey.
Key Features
Comprehensive Event Coverage: From Bitcoin’s inception to the most recent updates.
Custom View: Change label colors, styles, sizes, and fonts using the script’s settings.
Regular Updates: New events are added regularly to keep the history current.
Replay History
Use Bar Replay Mode to step through Bitcoin’s price history and see events unfold in sequence.
Follow the on-screen instructions for a more immersive experience.
Community Contributions
If you notice a significant event missing or misplaced on a particular date, feel free to leave a comment! Your suggestions will be considered for the next update.
To all Bitcoin enthusiasts, traders, and anyone eager to explore the history of cryptocurrency from its inception, I hope you enjoy this indicator :)
Bitcoin Logarithmic Growth Curve 2024The Bitcoin logarithmic growth curve is a concept used to analyze Bitcoin's price movements over time. The idea is based on the observation that Bitcoin's price tends to grow exponentially, particularly during bull markets. It attempts to give a long-term perspective on the Bitcoin price movements.
The curve includes an upper and lower band. These bands often represent zones where Bitcoin's price is overextended (upper band) or undervalued (lower band) relative to its historical growth trajectory. When the price touches or exceeds the upper band, it may indicate a speculative bubble, while prices near the lower band may suggest a buying opportunity.
Unlike most Bitcoin growth curve indicators, this one includes a logarithmic growth curve optimized using the latest 2024 price data, making it, in our view, superior to previous models. Additionally, it features statistical confidence intervals derived from linear regression, compatible across all timeframes, and extrapolates the data far into the future. Finally, this model allows users the flexibility to manually adjust the function parameters to suit their preferences.
The Bitcoin logarithmic growth curve has the following function:
y = 10^(a * log10(x) - b)
In the context of this formula, the y value represents the Bitcoin price, while the x value corresponds to the time, specifically indicated by the weekly bar number on the chart.
How is it made (You can skip this section if you’re not a fan of math):
To optimize the fit of this function and determine the optimal values of a and b, the previous weekly cycle peak values were analyzed. The corresponding x and y values were recorded as follows:
113, 18.55
240, 1004.42
451, 19128.27
655, 65502.47
The same process was applied to the bear market low values:
103, 2.48
267, 211.03
471, 3192.87
676, 16255.15
Next, these values were converted to their linear form by applying the base-10 logarithm. This transformation allows the function to be expressed in a linear state: y = a * x − b. This step is essential for enabling linear regression on these values.
For the cycle peak (x,y) values:
2.053, 1.268
2.380, 3.002
2.654, 4.282
2.816, 4.816
And for the bear market low (x,y) values:
2.013, 0.394
2.427, 2.324
2.673, 3.504
2.830, 4.211
Next, linear regression was performed on both these datasets. (Numerous tools are available online for linear regression calculations, making manual computations unnecessary).
Linear regression is a method used to find a straight line that best represents the relationship between two variables. It looks at how changes in one variable affect another and tries to predict values based on that relationship.
The goal is to minimize the differences between the actual data points and the points predicted by the line. Essentially, it aims to optimize for the highest R-Square value.
Below are the results:
It is important to note that both the slope (a-value) and the y-intercept (b-value) have associated standard errors. These standard errors can be used to calculate confidence intervals by multiplying them by the t-values (two degrees of freedom) from the linear regression.
These t-values can be found in a t-distribution table. For the top cycle confidence intervals, we used t10% (0.133), t25% (0.323), and t33% (0.414). For the bottom cycle confidence intervals, the t-values used were t10% (0.133), t25% (0.323), t33% (0.414), t50% (0.765), and t67% (1.063).
The final bull cycle function is:
y = 10^(4.058 ± 0.133 * log10(x) – 6.44 ± 0.324)
The final bear cycle function is:
y = 10^(4.684 ± 0.025 * log10(x) – -9.034 ± 0.063)
The main Criticisms of growth curve models:
The Bitcoin logarithmic growth curve model faces several general criticisms that we’d like to highlight briefly. The most significant, in our view, is its heavy reliance on past price data, which may not accurately forecast future trends. For instance, previous growth curve models from 2020 on TradingView were overly optimistic in predicting the last cycle’s peak.
This is why we aimed to present our process for deriving the final functions in a transparent, step-by-step scientific manner, including statistical confidence intervals. It's important to note that the bull cycle function is less reliable than the bear cycle function, as the top band is significantly wider than the bottom band.
Even so, we still believe that the Bitcoin logarithmic growth curve presented in this script is overly optimistic since it goes parly against the concept of diminishing returns which we discussed in this post:
This is why we also propose alternative parameter settings that align more closely with the theory of diminishing returns.
Our recommendations:
Drawing on the concept of diminishing returns, we propose alternative settings for this model that we believe provide a more realistic forecast aligned with this theory. The adjusted parameters apply only to the top band: a-value: 3.637 ± 0.2343 and b-parameter: -5.369 ± 0.6264. However, please note that these values are highly subjective, and you should be aware of the model's limitations.
Conservative bull cycle model:
y = 10^(3.637 ± 0.2343 * log10(x) - 5.369 ± 0.6264)
Bitcoin Futures vs. Spot Tri-Frame - Strategy [presentTrading]Prove idea with a backtest is always true for trading.
I developed and open-sourced it as an educational material for crypto traders to understand that the futures and spot spread may be effective but not be as effective as they might think. It serves as an indicator of sentiment rather than a reliable predictor of market trends over certain periods. It is better suited for specific trading environments, which require further research.
█ Introduction and How it is Different
The "Bitcoin Futures vs. Spot Tri-Frame Strategy" utilizes three different timeframes to calculate the Z-Score of the spread between BTC futures and spot prices on Binance and OKX exchanges. The strategy executes long or short trades based on composite Z-Score conditions across the three timeframes.
The spread refers to the difference in price between BTC futures and BTC spot prices, calculated by taking a weighted average of futures prices from multiple exchanges (Binance and OKX) and subtracting a weighted average of spot prices from the same exchanges.
BTCUSD 1D L/S Performance
█ Strategy, How It Works: Detailed Explanation
🔶 Calculation of the Spread
The spread is the difference in price between BTC futures and BTC spot prices. The strategy calculates the spread by taking a weighted average of futures prices from multiple exchanges (Binance and OKX) and subtracting a weighted average of spot prices from the same exchanges. This spread serves as the primary metric for identifying trading opportunities.
Spread = Weighted Average Futures Price - Weighted Average Spot Price
🔶 Z-Score Calculation
The Z-Score measures how many standard deviations the current spread is from its historical mean. This is calculated for each timeframe as follows:
Spread Mean_tf = SMA(Spread_tf, longTermSMA)
Spread StdDev_tf = STDEV(Spread_tf, longTermSMA)
Z-Score_tf = (Spread_tf - Spread Mean_tf) / Spread StdDev_tf
Local performance
🔶 Composite Entry Conditions
The strategy triggers long and short entries based on composite Z-Score conditions across all three timeframes:
- Long Condition: All three Z-Scores must be greater than the long entry threshold.
Long Condition = (Z-Score_tf1 > zScoreLongEntryThreshold) and (Z-Score_tf2 > zScoreLongEntryThreshold) and (Z-Score_tf3 > zScoreLongEntryThreshold)
- Short Condition: All three Z-Scores must be less than the short entry threshold.
Short Condition = (Z-Score_tf1 < zScoreShortEntryThreshold) and (Z-Score_tf2 < zScoreShortEntryThreshold) and (Z-Score_tf3 < zScoreShortEntryThreshold)
█ Trade Direction
The strategy allows the user to specify the trading direction:
- Long: Only long trades are executed.
- Short: Only short trades are executed.
- Both: Both long and short trades are executed based on the Z-Score conditions.
█ Usage
The strategy can be applied to BTC or Crypto trading on major exchanges like Binance and OKX. By leveraging discrepancies between futures and spot prices, traders can exploit market inefficiencies. This strategy is suitable for traders who prefer a statistical approach and want to diversify their timeframes to validate signals.
█ Default Settings
- Input TF 1 (60 minutes): Sets the first timeframe for Z-Score calculation.
- Input TF 2 (120 minutes): Sets the second timeframe for Z-Score calculation.
- Input TF 3 (180 minutes): Sets the third timeframe for Z-Score calculation.
- Long Entry Z-Score Threshold (3): Defines the threshold above which a long trade is triggered.
- Short Entry Z-Score Threshold (-3): Defines the threshold below which a short trade is triggered.
- Long-Term SMA Period (100): The period used to calculate the simple moving average for the spread.
- Use Hold Days (true): Enables holding trades for a specified number of days.
- Hold Days (5): Number of days to hold the trade before exiting.
- TPSL Condition (None): Defines the conditions for taking profit and stop loss.
- Take Profit (%) (30.0): The percentage at which the trade will take profit.
- Stop Loss (%) (20.0): The percentage at which the trade will stop loss.
By fine-tuning these settings, traders can optimize the strategy to suit their risk tolerance and trading style, enhancing overall performance.
