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" için komut dosyalarını ara
Bitcoin Cash - BCHABCSV Aggregate IndexAn index of both Bitcoin Cash ABC pre-fork and Bitcoin Cash ABC + Bitcoin Cash SV post-fork.
The pre-fork BCH used is from Bittrex, and Binance is used for ABC and SV afterwards.
Option to choose USDT or BTC pairing.
Instructions:
1. Load up a BCH chart from Bittrex, ex. 'BITTREX:BCHABCUSDT' or 'BITTREX:BCHSVBTC' for full chart history
2. Hide original candlesticks
3. Right click the price scale and untick 'Scale Price Chart Only'
Bitcoin Pine Script - Tom Hall StrategyThe Bitcoin script is a combination of crucial indicators that align across multiple timeframes.
How To Apply The Script:
Apply the script to your chart by clicking the ( Add to Favourite Scripts )\u2028
BSO = Buy Stop Order
The BSO symbol will appear once a valid trade opportunity presents itself.\u2028
Once the BSO candle closes it will provide you the parameters for a Buy Stop Order.
Orange Horizontal Line = Buy Stop Order Entry
Green Horizontal Line = Take Profit
Red Horizontal Line = Stop Loss
Key Information:
(1) The BSO is valid for a period of 24 hours, should price not trigger a live position the BSO must be cancelled.
(2) The horizontal lines that track price action are only relevant once a BSO candle has closed.
Alert System:
The alert system allows you to receive SMS / Email notifications in addition to a screen notification providing you information a BSO is required.
How To Apply The Alert System:
(1) Windows Press ( ALT + A ) / MacBook Press ( Option + A )
(2) Adjust the condition section from BTCUSD to Tom Hall Strategy\u2028
(3) Two crucial boxes will appear, The Lowest EMA and Buy Stop Order.
(4) Click create, this will allow you to receive Email / SMS notifications once a valid trade opportunity is available.\u2028
Profitable Edge:
Data From: 31st March 2013
Positions Executed: 76
Profitable Trades: 52
Losing Traders: 24\u2028
Risk / Reward: 1:1
Strike Rate / Profitable Edge: 68.43%
2013: 80% Profitable ( 10 Positions )
2014: 60% Profitable ( 5 Positions )
2015: 75% Profitable ( 16 Positions )
2016: 45% Profitable ( 20 Positions )
2017: 82.61% Profitable ( 23 Positions )
Style / Inputs:
All visible parameters can be adjusted to individual taste and preference.
Bitcoin Moving Average 10, 20, 60 MA (Bitcoin Multiple MA) ⓙMultiple Moving Average 10, 20, 60 MA, 비트코인 다중 MA
Comparing Alt Coin Prices to Bitcoin Price on the separate layout.
빨강 Red line = 1H
주황 Orange line = 4H
초록 Green line = 1D
알트코인 선택과 별도로, 아래에 비트코인 차트가 나옵니다.
알트코인 차트와 비트코인 차트를 비교하면서 투자할 수 있습니다.
릴리즈 노트: Bitcoin 가격은 Binance의 BTCUSDT 가격을 사용합니다.
Bitcoin Long/Short Ratio V2 + Bottom AlertVersion 2 of my Bitcoin Long/Short Ratio with the addition of a market bottom alert. Enjoy.
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
Google Trends: Bitcoin [Bitcoin CounterFlow]This script displays weekly Google Trends data for the term "Bitcoin". It can help visualize public interest over time and compare it with price action or other indicators. Data is manually updated each week based on Google Trends. Values range from 0 to 100, where 100 represents peak popularity for the selected term.
Use this indicator to observe how shifts in search volume correlate with market movements. It is not a trading signal by itself but can be useful for sentiment analysis.
Script created and published by Bitcoin CounterFlow.
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 SMA channels - quorraThis indicator is specifically designed to identify potential Bitcoin bottom zones based on historical data and market trends. By analyzing price cycles and key support levels, it helps traders and investors make informed decisions. This tool is tailored for optimal use on higher timeframes like the daily chart. (Don't forget to ensure your chart is set to logarithmic)
1. Simple Moving Average (SMA) Calculation and Gradient Coloring
The script begins by calculating the 350-period SMA (sma350), which serves as the foundation for identifying the market's overall trend. To make the SMA visually intuitive, a gradient color function is implemented. This function changes the SMA's color based on whether the current price (close) is above or below the SMA.
If the price is above the SMA, the line appears in gray.
If the price is below the SMA, the line takes on a darker red shade.
This gradient coloring helps traders quickly gauge market sentiment and momentum, as the SMA effectively acts as a dynamic trend line.
2. Fibonacci-Based Multipliers for SMA Levels
The indicator computes several levels based on Fibonacci multipliers of the 350-period SMA. These levels provide additional layers of insight into potential support and resistance zones. The multipliers range from small values like 0.144 (indicating closer proximity to the SMA) to larger values like 9 (representing distant extensions).
These Fibonacci levels are plotted using hidden lines, ensuring that the chart remains uncluttered while still allowing for strategic visualization through filled zones. For instance:
Levels like SMA x 0.144 to SMA x 0.355 are closer to the SMA and are categorized as potential buy zones.
Levels like SMA x 2 to SMA x 9 extend further and are considered sell zones.
3. Filling Areas to Visualize Zones
To enhance the visual representation, the script uses fill() functions to color the regions between specific Fibonacci levels:
Buy Zones: These areas are filled with a semi-transparent gray color (#5a5a5a) to indicate levels where prices are likely to bounce upward.
Sell Zones: Conversely, these areas are filled with a semi-transparent red color (#5f0000), signaling regions where prices may encounter resistance and reverse downward.
This layered approach helps traders identify actionable price ranges without overwhelming them with excessive visual elements.
4. Pivot Points and Their Visualization
The script includes a pivot point system for identifying local highs and lows. Depending on the selected source (High/Low or Close/Open), it calculates pivot highs and lows over a specified period (prd).
Pivot highs (ph) are marked above bars using downward-facing labels.
Pivot lows (pl) are marked below bars using upward-facing labels.
The pivot points are adjustable via user inputs, allowing traders to fine-tune the detection of significant price swings.
5. Support and Resistance Channel Analysis
A key feature of this indicator is its ability to identify and display support and resistance (S/R) levels. The script calculates the maximum allowable width of an S/R channel as a percentage of the price range over a 300-bar window. It then groups pivot points within these channels to derive high and low boundaries.
Resistance Levels: Represented by the upper bounds of channels and highlighted with a red color.
Support Levels: Represented by the lower bounds of channels and highlighted with a gray color.
These levels are dynamically adjusted based on user-defined parameters such as channel width, maximum S/R levels, and strength.
6. Advanced Input Customization
The indicator provides several user-configurable inputs to adapt it to different trading strategies:
Pivot Period (prd): Determines the sensitivity of pivot point calculations.
Channel Width: Controls the percentage width of S/R zones.
Maximum S/R Levels: Sets the maximum number of S/R zones displayed.
Line Style and Color Settings: Allows customization of the visual appearance of lines and labels.
7. Strength Filtering for S/R Levels
To ensure the reliability of identified S/R levels, the script incorporates a filtering mechanism based on strength. Strength is determined by the number of pivot points that fall within a channel. Levels with insufficient strength are excluded, ensuring that only significant S/R zones are displayed.
8. Practical Applications
This indicator can be applied in various trading strategies:
Trend Identification: The SMA and its gradient coloring provide a clear indication of the market's prevailing trend.
Support/Resistance Trading: The Fibonacci levels and S/R zones help traders identify potential entry and exit points.
Risk Management: By visualizing key levels, the indicator assists traders in setting stop-loss and take-profit levels effectively.
This script combines multiple technical analysis techniques into a single, visually intuitive tool. It is particularly useful for Bitcoin traders seeking to enhance their decision-making process by leveraging both trend and level-based analysis.
Although this indicator is specifically designed for Bitcoin, it can also be applied to stocks or altcoins. It works best on longer timeframes, such as the daily chart. When the price reaches specific support levels, it may be wise to activate a DCA bot or confirm the bottom using other indicators. This approach helps enhance decision-making and ensures a more strategic entry or exit from positions.
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 Trend Indicator█ Overview
The Trend Indicator script is designed to help traders identify the direction and strength of momentum in the price of a digital asset. By using historical price data, it calculates and provides daily signals indicating whether the asset is in an uptrend, downtrend, or no trend at all. The script can be applied to various cryptocurrencies, such as Bitcoin and Ether, using their respective price charts.
█ Key Concepts and Calculation Methodology
For calculations, the script uses the 180 most recent candles.
The Trend Indicator is calculated based on four moving average pairs (MAPs), which compare shorter-term and longer-term moving averages of the asset's price.
The moving averages are exponentially weighted, meaning more recent prices have a greater impact on the average than older prices. The half-life of the moving averages determines the weight decay.
The script uses the following moving average pairs:
1-day vs. 5-day
2.5-day vs. 10-day
5-day vs. 20-day
10-day vs. 40-day
█ Calculation Steps
Exponentially Weighted Moving Averages (EWMA):
Each moving average is calculated using an exponential decay factor and a normalization factor to adjust for the fixed window of 180 observations.
Component Inputs:
For each moving average pair, the script compares the shorter-term moving average to the longer-term moving average. If the shorter-term average is greater than or equal to the longer-term average, the component input is +1 (indicating an uptrend). If it is less, the input is -1 (indicating a downtrend).
Trend Indicator Value:
The script averages the four component inputs to produce a final value ranging from -1 to +1, representing the trend's direction and strength:
+1: Significant uptrend
+0.5: Uptrend
0: No trend
-0.5: Downtrend
-1: Significant downtrend
█ Learn More
For more information about the Bitcoin Trend Indicator and other trading tools, please visit my TradingView profile. Feel free to reach out with any questions or feedback.
Bitcoin Regression Price BoundariesTLDR
DCA into BTC at or below the blue line. DCA out of BTC when price approaches the red line. There's a setting to toggle the future extrapolation off/on.
INTRODUCTION
Regression analysis is a fundamental and powerful data science tool, when applied CORRECTLY . All Bitcoin regressions I've seen (Rainbow Log, Stock-to-flow, and non-linear models), have glaring flaws ... Namely, that they have huge drift from one cycle to the next.
Presented here, is a canonical application of this statistical tool. "Canonical" meaning that any trained analyst applying the established methodology, would arrive at the same result. We model 3 lines:
Upper price boundary (red) - Predicted the April 2021 top to within 1%
Lower price boundary (green)- Predicted the Dec 2022 bottom within 10%
Non-bubble best fit line (blue) - Last update was performed on Feb 28 2024.
NOTE: The red/green lines were calculated using solely data from BEFORE 2021.
"I'M INTRUIGED, BUT WHAT EXACTLY IS REGRESSION ANALYSIS?"
Quite simply, it attempts to draw a best-fit line over some set of data. As you can imagine, there are endless forms of equations that we might try. So we need objective means of determining which equations are better than others. This is where statistical rigor is crucial.
We check p-values to ensure that a proposed model is better than chance. When comparing two different equations, we check R-squared and Residual Standard Error, to determine which equation is modeling the data better. We check residuals to ensure the equation is sufficiently complex to model all the available signal. We check adjusted R-squared to ensure the equation is not *overly* complex and merely modeling random noise.
While most people probably won't entirely understand the above paragraph, there's enough key terminology in for the intellectually curious to research.
DIVING DEEPER INTO THE 3 REGRESSION LINES ABOVE
WARNING! THIS IS TECHNICAL, AND VERY ABBREVIATED
We prefer a linear regression, as the statistical checks it allows are convenient and powerful. However, the BTCUSD dataset is decidedly non-linear. Thus, we must log transform both the x-axis and y-axis. At the end of this process, we'll use e^ to transform back to natural scale.
Plotting the log transformed data reveals a crucial visual insight. The best fit line for the blowoff tops is different than for the lower price boundary. This is why other models have failed. They attempt to model ALL the data with just one equation. This causes drift in both the upper and lower boundaries. Here we calculate these boundaries as separate equations.
Upper Boundary (in red) = e^(3.24*ln(x)-15.8)
Lower Boundary (green) = e^(0.602*ln^2(x) - 4.78*ln(x) + 7.17)
Non-Bubble best fit (blue) = e^(0.633*ln^2(x) - 5.09*ln(x) +8.12)
* (x) = The number of days since July 18 2010
Anyone familiar with Bitcoin, knows it goes in cycles where price goes stratospheric, typically measured in months; and then a lengthy cool-off period measured in years. The non-bubble best fit line methodically removes the extreme upward deviations until the residuals have the closest statistical semblance to normal data (bell curve shaped data).
Whereas the upper/lower boundary only gets re-calculated in hindsight (well after a blowoff or capitulation occur), the Non-Bubble line changes ever so slightly with each new datapoint. The last update to this line was made on Feb 28, 2024.
ENOUGH NERD TALK! HOW CAN I APPLY THIS?
In the simplest terms, anything below the blue line is a statistical buying opportunity. The closer you approach the green line (the lower boundary) the more statistically strong that opportunity is. As price approaches the red line, is a growing statistical likelyhood/danger of an imminent blowoff top.
So a wise trader would DCA (dollar cost average) into Bitcoin below the blue line; and would DCA out of Bitcoin as it approaches the red line. Historically, you may or may not have a large time-window during points of maximum opportunity. So be vigilant! Anything within 10-20% of the boundary should be regarded as extreme opportunity.
Note: You can toggle the future extrapolation of these lines in the settings (default on).
CLOSING REMARKS
Keep in mind this is a pure statistical analysis. It's likely that this model is probing a complex, real economic process underlying the Bitcoin price. Statistical models like this are most accurate during steady state conditions, where the prevailing fundamentals are stable. (The astute observer will note, that the regression boundaries held despite the economic disruption of 2020).
Thus, it cannot be understated: Should some drastic fundamental change occur in the underlying economic landscape of cryptocurrency, Bitcoin itself, or the broader economy, this model could drastically deviate, and become significantly less accurate.
Furthermore, the upper/lower boundaries cross in the year 2037. THIS MODEL WILL EVENTUALLY BREAK DOWN. But for now, given that Bitcoin price moves on the order of 2000% from bottom to top, it's truly remarkable that, using SOLELY pre-2021 data, this model was able to nail the top/bottom within 10%.
Bitcoin Pi Cycle Top Indicator - Daily Timeframe Only1 Day Timeframe Only
The Bitcoin Pi Cycle Top Indicator has garnered attention for its historical effectiveness in identifying the timing of Bitcoin's market cycle peaks with remarkable precision, typically within a margin of 3 days.
It utilizes a specific combination of moving averages—the 111-day moving average and a 2x multiple of the 350-day moving average—to signal potential tops in the Bitcoin market.
The 111-day moving average (MA): This shorter-term MA is chosen to reflect more recent price action and trends within the Bitcoin market.
The 350-day moving average (MA) multiplied by 2: This longer-term MA is adjusted to capture broader market trends and cycles over an extended period.
The key premise behind the Bitcoin Pi Cycle Top Indicator is that a potential market top for Bitcoin can be signaled when the 111-day MA crosses above the 350-day MA (which has been doubled). Historically, this crossover event has shown a remarkable correlation with the peaks of Bitcoin's price cycles, making it a tool of interest for traders and investors aiming to anticipate significant market shifts.
#Bitcoin
Bitcoin Price to Volume per $1 FeeTransaction value to transaction fee:
The Bitcoin network's efficiency, usability and volume scalability has been improving over time and this can be measured by dividing the average transaction volume by the transaction fee.
The indicator give us:
Price to volume per $1 fee = BTC price / (avg tx value / avg tx fee)
A low ratio of "Price to volume per $1 fee" indicates that the Bitcoin network is being used for high volumes in comparison to the Bitcoin price, which means that the network is cost-effective compared to the price. On the other hand, a high "Price to volume per $1 fee" suggests that the average transaction size is smaller than the price of Bitcoin, which means that the network is less cost-effective compared to the Bitcoin price.
Note that the dynamics of transaction fees may change over time as new use cases emerge in the Bitcoin chain. These use cases include L2s such as Stacks, where DeFi applications can run, and Bitcoin Ordinals.
It's worth mentioning that Bitcoin is not only a cost-effective way of transferring value, but also highly energy efficient. Despite receiving criticism for its energy consumption, when we compare its energy usage to other industries (such as banking and gold) and correlate it with the transaction volumes, we can easily conclude that Bitcoin's energy efficiency is remarkable when compared to other methods of transferring value.
Bitcoin Google Trends OverlayThis indicator overlays Bitcoin Google trends data starting from 16/12/2018 until 10/12/2023. To have more recent data, you will need to update the data points manually.
If it is not showing properly, you need to plot the indicator to a new scale. Try also to use a logarithmic scale to better correlate the Bitcoin Google Trends data.
Interpretation:
Google Trends data and the Bitcoin price are very correlated. Google Trends data is a good indicator of market sentiment, but it usually lags.
Bitcoin Correlation MapHello everyone,
This indicator shows the correlation coefficients of altcoins with bitcoin in a table.
What is the correlation coefficient?
The correlation coefficient is a value that takes a value between 0 and 1 when a parity makes similar movements with the reference parity, and takes a value between 0 and -1 when it makes opposite movements.
In order to obtain more meaningful and real-time results in this indicator, the weighted average of the correlation values of the last 200bar was used. You can change the bar length as you wish. With the correlation value, you can see the parities that have similar movements with bitcoin and integrate them into your strategy.
You can change the coin list as you wish, and you can also calculate their correlation with etherium instead of bitcoin .
The indicator shows the correlation value of 36 altcoins at the moment.
The indicator indicates the color of the correlated parities as green and the color of the inversely correlated parities as red.
Cheers
Bitcoin Miner Extreme SellingThis script is for identifying extreme selling. Judging by the chart, Bitcoin miners often (not always) sell hard for two reasons: to take profit into parabolic price rises, or to stay solvent when the price is very low.
Extreme selling thus often coincides with long-term tops and bottoms in Bitcoin price. This can be a useful EXTRA data point when trying to time long-term Bitcoin spot or crypto equity investment (NOT advice, you remain responsible, etc). The difference between selling measured in BTC and in USD gives a reasonable idea of whether miners are selling to make a profit or to stay solvent.
CREDITS
The idea for using the ratio of miner outflows to reserves comes from the "Bitcoin Miner Sell Pressure" script by the pioneering capriole_charles.
The two request.security calls are identical. Another similarity is that you have to sum the outflows to make it make sense. But it doesn't make much difference, it turns out from testing, to use an average of the reserves, so I didn't. All other code is different.
The script from capriole_charles uses Bollinger bands to highlight periods when sell pressure is high, uses a rolling 30-day sum, and only uses the BTC metrics.
My script uses a configurable 2-6 week rolling sum (there's nothing magical about one month), uses different calculations, and uses BTC, USD, and composite metrics.
INPUTS
Rolling Time Basis : Determines how much data is rolled up. At the lowest level, daily data is too volatile. If you choose, e.g., 1 week, then the indicator displays the relative selling on a weekly basis. Longer time periods, obviously, are smoother but delayed, while shorter time periods are more reactive. There is no "real" time period, only an explicit interpretation.
Show Data > Outflows : Displays the relative selling data, along with a long-term moving average. You might use this option if you want to compare the "real" heights of peaks across history.
Show Data > Delta (the default): Only the difference between the relative selling and the long-term moving average is displayed, along with an average of *that*. This is more signal and less noise.
Base Currency : Configure whether the calculations use BTC or USD as the metric. This setting doesn't use the BTC price at all; it switches the data requested from INTOTHEBLOCK.
If you choose Composite (the default), the script combines BTC and USD together in a relative way (you can't simply add them, as USD is a much bigger absolute value).
In Composite mode, the peaks are coloured red if BTC selling is higher than USD, which usually indicates forced selling, and green if USD is higher, which usually indicates profit-taking. This categorisation is not perfectly accurate but it is interesting insomuch as it is derived from block data and not Bitcoin price.
In BTC or USD mode, a gradient is used to give a rough visual idea of how far from the average the current value is, and to make it look pretty.
USAGE NOTES
Because of the long-term moving averages, the length of the chart does make a difference. I recommend running the script on the longest Bitcoin chart, ticker BLX.
To use it to compare selling with pivots in crypto equities, use a split chart: one BLX with the indicator applied, and one with the equity of your choice. Sync Interval, Crosshair, Time, and Date Range, but not Symbol.
Bitcoin Golden Pi CyclesTops are signaled by the fast top MA crossing above the slow top MA, and bottoms are signaled by the slow bottom MA crossing above the fast bottom MA. Alerts can be set on top and bottom prints. Does not repaint.
Similar to the work of Philip Swift regarding the Bitcoin Pi Cycle Top, I’ve recently come across a similar mathematically curious ratio that corresponds to Bitcoin cycle bottoms. This ratio was extracted from skirmantas’ Bitcoin Super Cycle indicator . Cycle bottoms are signaled when the 700D SMA crosses above the 137D SMA (because this indicator is closed source, these moving averages were reverse-engineered). Such crossings have historically coincided with the January 2015 and December 2018 bottoms. Also, although yet to be confirmed as a bottom, a cross occurred June 19, 2022 (two days prior to this article)
The original pi cycle uses the doubled 350D SMA and the 111D SMA . As pointed out this gives the original pi cycle top ratio:
350/111 = 3.1532 ≈ π
Also, as noted by Swift, 111 is the best integer for dividing 350 to approximate π. What is mathematically interesting about skirmanta’s ratio?
700/138 = 5.1095
After playing around with this for a while I realized that 5.11 is very close to the product of the two most numerologically significant geometrical constants, π and the golden ratio, ϕ:
πϕ = 5.0832
However, 138 turns out to be the best integer denominator to approximate πϕ:
700/138 = 5.0725 ≈ πϕ
This is what I’ve dubbed the Bitcoin Golden Pi Bottom Ratio.
In the spirit of numerology I must mention that 137 does have some things going for it: it’s a prime number and is very famously almost exactly the reciprocal of the fine structure constant (α is within 0.03% of 1/137).
Now why 350 and 700 and not say 360 and 720? After all, 360 is obviously much more numerologically significant than 350, which is proven by the fact that 360 has its own wikipedia page, and 350 does not! Using 360/115 and 720/142, which are also approximations of π and πϕ respectively, this also calls cycle tops and bottoms.
There are infinitely many such ratios that could work to approximate π and πϕ (although there are a finite number whose daily moving averages are defined). Further analysis is needed to find the range(s) of numerators (the numerator determines the denominator when maintaining the ratio) that correctly produce bottom and top signals.
Bitcoin Risk RangeThis is an extension of the original 'Bitcoin Bubble' indicator I previously made, but shows the necessary price required to reach a range of bitcoin's bubble level in the short term. I recommend using this metric with a daily timeframe to have an adequate amount of data.
Bitcoin BanditIntroducing "Bitcoin Bandit".
The market beating trading algorithm for Bitcoin .
"Bitcoin Bandit" buys and sells based on three proprietary indicators:
• Futures contract data
• Accumulation areas and various moving averages.
• Bitcoin hash rate
The indicator is unique because it doesn't give significant weight to historical price to predict future price action; instead it uses BTC hash rate momentum and futures contract data from BTCUSDPERP (transformed through various internal processes) as proxies for sentiment to look for buy and sell zones, then uses accumulation of moving averages as supporting data for signal delivery.
The strategy was built on two years of Binance data and and backtested on five years of Bitcoin data (Coinbase: BTCUSD ).
Finally, the strategy was validated over multiple investment time frames (5 years, 2 years, 1 year) without prior parameter adjustment.
Strategy backtesting checks include:
• 0.60% trading commission fees (the highest possible).
• No Heiken-Ashi candles (to preserve accuracy)
• No Stop-Losses
• Market orders only
The results speak for themselves.
See the positive excess return from the “Bitcoin Bandit” strategy returns versus a simple Bitcoin “Buy-and-Hold” strategy. "Bitcoin Bandit" is designed to function only on the Daily time frame of the BTCUSD trading pair.
Does it Repaint?
• Our indicator does NOT repaint. Although while setting an alert it may pop up the repaint alert, please take into consideration that once a signal is fired on a "CLOSED BAR", the signals will never disappear, they do not repaint.
What Markets is it usable with?
• BTCUSD on the Daily timeframe .
• Bitcoin Bandit can be applied to any chart or altcoin, but results will be unpredictable as this indicator is designed specifically for Bitcoin trading.
How to use:
• Simply plug and play it to your chart. You can also connect TV alerts with a bot and let it run. Please be aware that SLIPPAGE time is important, If you run a bot on this indicator you HAVE to know that the buy/sell price will be on the bar AFTER the Candle close (For example: the BUY/SELL alert is on a candle, the buy/sell your bot or you will execute WILL be in the following candle depending on your trading system. Bitcoin Bandit only works on the Daily timeframe on the BTCUSD trading pair. Please contact us if you do not understand how to use it.
Disclaimer: Nothing stated is financial advice, and is purely for education purposes. We do not promise all trades are profitable, the use of this indicator is up to your own judgement and liability.
