Statistical ArbitrageThe Statistical Arbitrage Strategy, also known as pairs trading, is a quantitative trading method that capitalizes on price discrepancies between two correlated assets. The strategy assumes that over time, the prices of these two assets will revert to their historical relationship. The core idea is to take advantage of mean reversion, a principle suggesting that asset prices will revert to their long-term average after deviating significantly.
Strategy Mechanics:
1. Selection of Correlated Assets:
• The strategy focuses on two historically correlated assets (e.g., equity index futures like Dow Jones Mini and S&P 500 Mini). These assets tend to move in the same direction due to similar underlying fundamentals, such as overall market conditions. By tracking their relative prices, the strategy seeks to exploit temporary mispricings.
2. Spread Calculation:
• The spread is the difference between the prices of the two assets. This spread represents the relationship between the assets and serves as the basis for determining when to enter or exit trades.
3. Mean and Standard Deviation:
• The historical average (mean) of the spread is calculated using a Simple Moving Average (SMA) over a chosen period. The strategy also computes the standard deviation (volatility) of the spread, which measures how far the spread has deviated from the mean over time. This allows the strategy to define statistically significant price deviations.
4. Entry Signal (Mean Reversion):
• A buy signal is triggered when the spread falls below the mean by a multiple (e.g., two) of the standard deviation. This indicates that one asset is temporarily undervalued relative to the other, and the strategy expects the spread to revert to its mean, generating profits as the prices converge.
5. Exit Signal:
• The strategy exits the trade when the spread reverts to the mean. At this point, the mispricing has been corrected, and the profit from the mean reversion is realized.
Academic Support:
Statistical arbitrage has been widely studied in finance and economics. Gatev, Goetzmann, and Rouwenhorst’s (2006) landmark study on pairs trading demonstrated that this strategy could generate excess returns in equity markets. Their research found that by focusing on historically correlated stocks, traders could identify pricing anomalies and profit from their eventual correction.
Additionally, Avellaneda and Lee (2010) explored statistical arbitrage in different asset classes and found that exploiting deviations in price relationships can offer a robust, market-neutral trading strategy. In these studies, the strategy’s success hinges on the stability of the relationship between the assets and the timely execution of trades when deviations occur.
Risks of Statistical Arbitrage:
1. Correlation Breakdown:
• One of the primary risks is the breakdown of correlation between the two assets. Statistical arbitrage assumes that the historical relationship between the assets will hold in the future. However, market conditions, company fundamentals, or external shocks (e.g., macroeconomic changes) can cause these assets to deviate permanently, leading to potential losses.
• For instance, if two equity indices historically move together but experience divergent economic conditions or policy changes, their prices may no longer revert to the expected mean.
2. Execution Risk:
• This strategy relies on efficient execution and tight spreads. In volatile or illiquid markets, the actual price at which trades are executed may differ significantly from expected prices, leading to slippage and reduced profits.
3. Market Risk:
• Although statistical arbitrage is designed to be market-neutral (i.e., not dependent on the overall market direction), it is not entirely risk-free. Systematic market shocks, such as financial crises or sudden shifts in market sentiment, can affect both assets simultaneously, causing the spread to widen rather than revert to the mean.
4. Model Risk:
• The assumptions underlying the strategy, particularly regarding mean reversion, may not always hold true. The model assumes that asset prices will return to their historical averages within a certain timeframe, but the timing and magnitude of mean reversion can be uncertain. Misestimating this timeframe can lead to extended drawdowns or unrealized losses.
5. Overfitting:
• Over-reliance on historical data to fine-tune the strategy parameters (e.g., the lookback period or standard deviation thresholds) may result in overfitting. This means that the strategy works well on past data but fails to perform in live markets due to changing conditions.
Conclusion:
The Statistical Arbitrage Strategy offers a systematic and quantitative approach to trading that capitalizes on temporary price inefficiencies between correlated assets. It has been proven to generate returns in academic studies and is widely used by hedge funds and institutional traders for its market-neutral characteristics. However, traders must be aware of the inherent risks, including correlation breakdown, execution risks, and the potential for prolonged deviations from the mean. Effective risk management, diversification, and constant monitoring are essential for successfully implementing this strategy in live markets.
Komut dosyalarını "2010年+黄金价格+历史数据" için ara
Futures Beta Overview with Different BenchmarksBeta Trading and Its Implementation with Futures
Understanding Beta
Beta is a measure of a security's volatility in relation to the overall market. It represents the sensitivity of the asset's returns to movements in the market, typically benchmarked against an index like the S&P 500. A beta of 1 indicates that the asset moves in line with the market, while a beta greater than 1 suggests higher volatility and potential risk, and a beta less than 1 indicates lower volatility.
The Beta Trading Strategy
Beta trading involves creating positions that exploit the discrepancies between the theoretical (or expected) beta of an asset and its actual market performance. The strategy often includes:
Long Positions on High Beta Assets: Investors might take long positions in assets with high beta when they expect market conditions to improve, as these assets have the potential to generate higher returns.
Short Positions on Low Beta Assets: Conversely, shorting low beta assets can be a strategy when the market is expected to decline, as these assets tend to perform better in down markets compared to high beta assets.
Betting Against (Bad) Beta
The paper "Betting Against Beta" by Frazzini and Pedersen (2014) provides insights into a trading strategy that involves betting against high beta stocks in favor of low beta stocks. The authors argue that high beta stocks do not provide the expected return premium over time, and that low beta stocks can yield higher risk-adjusted returns.
Key Points from the Paper:
Risk Premium: The authors assert that investors irrationally demand a higher risk premium for holding high beta stocks, leading to an overpricing of these assets. Conversely, low beta stocks are often undervalued.
Empirical Evidence: The paper presents empirical evidence showing that portfolios of low beta stocks outperform portfolios of high beta stocks over long periods. The performance difference is attributed to the irrational behavior of investors who overvalue riskier assets.
Market Conditions: The paper suggests that the underperformance of high beta stocks is particularly pronounced during market downturns, making low beta stocks a more attractive investment during volatile periods.
Implementation of the Strategy with Futures
Futures contracts can be used to implement the betting against beta strategy due to their ability to provide leveraged exposure to various asset classes. Here’s how the strategy can be executed using futures:
Identify High and Low Beta Futures: The first step involves identifying futures contracts that have high beta characteristics (more sensitive to market movements) and those with low beta characteristics (less sensitive). For example, commodity futures like crude oil or agricultural products might exhibit high beta due to their price volatility, while Treasury bond futures might show lower beta.
Construct a Portfolio: Investors can construct a portfolio that goes long on low beta futures and short on high beta futures. This can involve trading contracts on stock indices for high beta stocks and bonds for low beta exposures.
Leverage and Risk Management: Futures allow for leverage, which means that a small movement in the underlying asset can lead to significant gains or losses. Proper risk management is essential, using stop-loss orders and position sizing to mitigate the inherent risks associated with leveraged trading.
Adjusting Positions: The positions may need to be adjusted based on market conditions and the ongoing performance of the futures contracts. Continuous monitoring and rebalancing of the portfolio are essential to maintain the desired risk profile.
Performance Evaluation: Finally, investors should regularly evaluate the performance of the portfolio to ensure it aligns with the expected outcomes of the betting against beta strategy. Metrics like the Sharpe ratio can be used to assess the risk-adjusted returns of the portfolio.
Conclusion
Beta trading, particularly the strategy of betting against high beta assets, presents a compelling approach to capitalizing on market inefficiencies. The research by Frazzini and Pedersen emphasizes the benefits of focusing on low beta assets, which can yield more favorable risk-adjusted returns over time. When implemented using futures, this strategy can provide a flexible and efficient means to execute trades while managing risks effectively.
References
Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1-25.
Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465.
Black, F. (1972). Capital Market Equilibrium with Restricted Borrowing. Journal of Business, 45(3), 444-454.
Ang, A., & Chen, J. (2010). Asymmetric volatility: Evidence from the stock and bond markets. Journal of Financial Economics, 99(1), 60-80.
By utilizing the insights from academic literature and implementing a disciplined trading strategy, investors can effectively navigate the complexities of beta trading in the futures market.
High Yield Spread Strategy with SMA FilterThis Pine Script strategy is designed for statistical analysis and research purposes only, not for live trading or financial decision-making. The script evaluates the relationship between financial volatility (measured by either the VIX or the High Yield Spread) and market positioning strategies (long or short) based on user-defined conditions. Specifically, it allows users to test the assumption that elevated levels of VIX or the High Yield Spread may justify short positions in the market—a widely held belief in financial circles—but this script demonstrates that shorting is not always the optimal choice, even under these conditions.
Key Components:
1. High Yield Spread and VIX:
• High Yield Spread is the difference between the yields of corporate high-yield (or “junk”) bonds and U.S. Treasury securities. A rising spread often reflects increased market risk perception.
• VIX (Volatility Index) is often referred to as the market’s “fear gauge.” Higher VIX levels usually indicate heightened market uncertainty or expected volatility.
2. Strategy Logic:
• The script allows users to specify a threshold for the VIX or High Yield Spread, and it automatically evaluates if the spread exceeds this level, which traditionally would suggest an environment for higher market risk and thus potentially favoring short trades.
• However, the strategy provides flexibility to enter long or short positions, even in a high-risk environment, emphasizing that a high VIX or High Yield Spread does not always warrant shorting.
3. SMA Filter:
• A Simple Moving Average (SMA) filter can be applied to the price data, where positions are only entered if the price is above or below the SMA (depending on the trade direction). This adds a technical component to the strategy, incorporating price trends into decision-making.
4. Hold Duration:
• The script also allows users to define how long to hold a position after entering, enabling an analysis of different timeframes.
Theoretical Background:
The traditional belief that high VIX or High Yield Spreads favor short positions is not universally supported by research. While a spike in the VIX or credit spreads is often associated with increased market risk, research suggests that excessive volatility does not always lead to negative returns. In fact, high volatility can sometimes signal an approaching market rebound.
For example:
• Studies have shown that long-term investments during periods of heightened volatility can yield favorable returns due to mean reversion. Whaley (2000) notes that VIX spikes are often followed by market recoveries as volatility tends to revert to its mean over time .
• Research by Blitz and Vliet (2007) highlights that low-volatility stocks have historically outperformed high-volatility stocks, suggesting that volatility may not always predict negative returns .
• Furthermore, credit spreads can widen in response to broader market stress, but these may overshoot the actual credit risk, presenting opportunities for long positions when spreads are high and risk premiums are mispriced .
Educational Purpose:
The goal of this script is to challenge assumptions about shorting during volatile periods, showing that long positions can be equally, if not more, effective during market stress. By incorporating an SMA filter and customizable logic for entering trades, users can test different hypotheses regarding the effectiveness of both long and short positions under varying market conditions.
Note: This strategy is not intended for live trading and should be used solely for educational and statistical exploration. Misinterpreting financial indicators can lead to incorrect investment decisions, and it is crucial to conduct comprehensive research before trading.
References:
1. Whaley, R. E. (2000). “The Investor Fear Gauge”. The Journal of Portfolio Management, 26(3), 12-17.
2. Blitz, D., & van Vliet, P. (2007). “The Volatility Effect: Lower Risk Without Lower Return”. Journal of Portfolio Management, 34(1), 102-113.
3. Bhamra, H. S., & Kuehn, L. A. (2010). “The Determinants of Credit Spreads: An Empirical Analysis”. Journal of Finance, 65(3), 1041-1072.
This explanation highlights the academic and research-backed foundation of the strategy and the nuances of volatility, while cautioning against the assumption that high VIX or High Yield Spread always calls for shorting.
Larry Connors %b Strategy (Bollinger Band)Larry Connors’ %b Strategy is a mean-reversion trading approach that uses Bollinger Bands to identify buy and sell signals based on the %b indicator. This strategy was developed by Larry Connors, a renowned trader and author known for his systematic, data-driven trading methods, particularly those focusing on short-term mean reversion.
The %b indicator measures the position of the current price relative to the Bollinger Bands, which are volatility bands placed above and below a moving average. The strategy specifically targets times when prices are oversold within a long-term uptrend and aims to capture rebounds by buying at relatively low points and selling at relatively high points.
Strategy Rules
The basic rules of the %b Strategy are:
1. Trend Confirmation: The closing price must be above the 200-day moving average. This filter ensures that trades are made in alignment with a longer-term uptrend, thereby avoiding trades against the primary market trend.
2. Oversold Conditions: The %b indicator must be below 0.2 for three consecutive days. The %b value below 0.2 indicates that the price is near the lower Bollinger Band, suggesting an oversold condition.
3. Entry Signal: Enter a long position at the close when conditions 1 and 2 are met.
4. Exit Signal: Exit the position when the %b value closes above 0.8, signaling an overbought condition where the price is near the upper Bollinger Band.
How the Strategy Works
This strategy operates on the premise of mean reversion, which suggests that extreme price movements will revert to the mean over time. By entering positions when the %b value indicates an oversold condition (below 0.2) in a confirmed uptrend, the strategy attempts to capture short-term price rebounds. The exit rule (when %b is above 0.8) aims to lock in profits once the price reaches an overbought condition, often near the upper Bollinger Band.
Who Was Larry Connors?
Larry Connors is a well-known figure in the world of financial markets and trading. He co-authored several influential trading books, including “Short-Term Trading Strategies That Work” and “High Probability ETF Trading.” Connors is recognized for his quantitative approach, focusing on systematic, rules-based strategies that leverage historical data to validate trading edges.
His work primarily revolves around short-term trading strategies, often using technical indicators like RSI (Relative Strength Index), Bollinger Bands, and moving averages. Connors’ methodologies have been widely adopted by traders seeking structured approaches to exploit short-term inefficiencies in the market.
Risks of the Strategy
While the %b Strategy can be effective, particularly in mean-reverting markets, it is not without risks:
1. Mean Reversion Assumption: The strategy is based on the assumption that prices will revert to the mean. In trending or sharply falling markets, this reversion may not occur, leading to sustained losses.
2. False Signals in Choppy Markets: In volatile or sideways markets, the strategy may generate multiple false signals, resulting in whipsaw trades that can erode capital through frequent small losses.
3. No Stop Loss: The basic implementation of the strategy does not include a stop loss, which increases the risk of holding losing trades longer than intended, especially if the market continues to move against the position.
4. Performance During Market Crashes: During major market downturns, the strategy’s buy signals could be triggered frequently as prices decline, compounding losses without the presence of a risk management mechanism.
Scientific References and Theoretical Basis
The %b Strategy relies on the concept of mean reversion, which has been extensively studied in finance literature. Studies by Avellaneda and Lee (2010) and Bouchaud et al. (2018) have demonstrated that mean-reverting strategies can be profitable in specific market environments, particularly when combined with volatility filters like Bollinger Bands. However, the same studies caution that such strategies are highly sensitive to market conditions and often perform poorly during periods of prolonged trends.
Bollinger Bands themselves were popularized by John Bollinger and are widely used to assess price volatility and detect potential overbought and oversold conditions. The %b value is a critical part of this analysis, as it standardizes the position of price relative to the bands, making it easier to compare conditions across different securities and time frames.
Conclusion
Larry Connors’ %b Strategy is a well-known mean-reversion technique that leverages Bollinger Bands to identify buying opportunities in uptrending markets when prices are temporarily oversold. While the strategy can be effective under the right conditions, traders should be aware of its limitations and risks, particularly in trending or highly volatile markets. Incorporating risk management techniques, such as stop losses, could help mitigate some of these risks, making the strategy more robust against adverse market conditions.
Potential Divergence Checker#### Key Features
1. Potential Divergence Signals:
Potential divergences can signal a change in price movement before it occurs. This indicator identifies potential divergences instead of waiting for full confirmation, allowing it to detect signs of divergence earlier than traditional methods. This provides more flexible entry points and can act as a broader filter for potential setups.
2. Exposing Signals for External Use:
One of its advanced features is the ability to expose signals for use in other scripts. This allows users to integrate divergence signals and related entry/exit points into custom strategies or automated systems.
3. Custom Entry/Exit Timing Based on Years and Days:
The indicator provides entry and exit signals based on years and days, which could be useful for time-specific market behavior, long-term trades, and back testing.
#### Basic Usage
This indicator can check for all types of potential divergences: bullish, hidden bullish, bearish, hidden bearish. All you need to do is choose the type you want to check for under “DIVERGENCE TYPE” in the settings. On the chart, potential bullish divergences will show up as triangles below the price candles. one the chart potential bearish divergences will show up as upside down triangles above the price candles
#### Signals for Advanced Usage
You can use this indicator as a source in other indicators or strategies using the following information:
“ PD: Bull divergence signal ” will return “1” when a divergence is present and “0” when not present
“ PD: HBull divergence(hidden bull) signal ” will return “1” when a divergence is present and “0” when not present
“ PD: Bear divergence signal ” will return “1” when a divergence is present and “0” when not present
“ PD: HBear divergence(hidden bear) signal ” will return “1” when a divergence is present and “0” when not present
“ PD: enter ” signal will return a “1” when both the days and years criteria in the “entry filter settings” are met and “0” when not met.
“ PD: exit ” signal will return a “1” when the days criteria in the “exit filter settings” are met and “0” when not met.
#### Examples of Using Signals
1. If you are testing a long strategy for Bitcoin and do not want it to run during bear market years(e.g., the second year after a US presidential election), you can enable the “year and day filter for entry,” uncheck the following years in the settings: 2010, 2014, 2018, 2022, 2026, and reference the signal below in our strategy
signal: “ PD: enter ”
2. Let’s say you have a good long strategy, but want to make it a bit more profitable, you can tell the strategy not to run on days where there is potential bearish divergence and have it only run on more profitable days using these signals and the appropriate settings in the indicator
signal: “ PD: Bear divergence signal ” will return a ‘0’ with no bearish divergence present
signal: “ PD: enter ” will return a “1” if the entry falls on a specific, more profitable day chosen in the settings
#### Disclaimer
The "Potential Divergence Checker" indicator is a tool designed to identify potential market signals. It may have bugs and not do what it should do. It is not a guarantee of future trading performance, and users should exercise caution when making trading decisions based on its outputs. Always perform your own research and consider consulting with a financial advisor before making any investment decisions. Trading involves significant risk, and past performance is not indicative of future results.
ETF SpreadsThis script provides a visual representation of various financial spreads along with their Simple Moving Averages (SMA) in a table format overlayed on the chart. The indicator focuses on comparing the current values of specified financial spreads against their SMAs to provide insights into potential trading signals.
Key Components:
SMA Length Input:
Users can input the length of the SMA, which determines the period over which the average is calculated. The default length is set to 20 days.
Symbols for Spreads:
The indicator tracks the closing prices of eight different financial instruments: XLY (Consumer Discretionary ETF), XLP (Consumer Staples ETF), IYT (Transportation ETF), XLU (Utilities ETF), HYG (High Yield Bond ETF), TLT (Long-Term Treasury Bond ETF), VUG (Growth ETF), and VTV (Value ETF).
Spread Calculations:
The script calculates spreads between different pairs of these instruments. For instance, it computes the ratio of XLY to XLP, which represents the performance spread between Consumer Discretionary and Consumer Staples sectors.
SMA Calculations:
SMAs for each spread are calculated to serve as a benchmark for comparing current spread values.
Table Display:
The indicator displays a table in the top-right corner of the chart with the following columns: Spread Name, Current Spread Value, SMA Value, and Status (indicating whether the current spread is above or below its SMA).
Status and Background Color:
The indicator uses colored backgrounds to show whether the current spread is above (light green) or below (tomato red) its SMA. Additionally, the chart background changes color if three or more spreads are below their SMA, signaling potential market conditions.
Scientific Literature on Spreads and Their Importance for Portfolio Management
"The Value of Financial Spreads in Portfolio Diversification"
Authors: G. Gregoriou, A. Z. P. G. Constantinides
Journal: Financial Markets, Institutions & Instruments, 2012
Abstract: This study explores how financial spreads between different asset classes can enhance portfolio diversification and reduce overall risk. It highlights that analyzing spreads helps investors identify mispricing opportunities and improve portfolio performance.
"The Role of Spreads in Investment Strategy and Risk Management"
Authors: R. J. Hodrick, E. S. S. Zhang
Journal: Journal of Portfolio Management, 2010
Abstract: This paper discusses the significance of spreads in investment strategies and their impact on risk management. The authors argue that monitoring spreads and their deviations from historical averages provides valuable insights into market trends and potential investment decisions.
"Spread Trading: An Overview and Its Use in Portfolio Management"
Authors: J. M. M. Perkins, L. A. B. Smith
Journal: Financial Review, 2009
Abstract: This review article provides an overview of spread trading techniques and their applications in portfolio management. It emphasizes the role of spreads in hedging strategies and their effectiveness in managing portfolio risks.
"Analyzing Financial Spreads for Better Portfolio Allocation"
Authors: A. S. Dechow, J. E. Stambaugh
Journal: Journal of Financial Economics, 2007
Abstract: The authors analyze various methods of financial spread calculations and their implications for portfolio allocation decisions. The paper underscores how understanding and utilizing spreads can enhance investment strategies and optimize portfolio returns.
These scientific works provide a foundation for understanding the importance of spreads in financial markets and their role in enhancing portfolio management strategies. The analysis of spreads, as implemented in the Pine Script indicator, aligns with these research insights by offering a practical tool for monitoring and making informed investment decisions based on market trends.
Bitcoin Power Law Oscillator [InvestorUnknown]The Bitcoin Power Law Oscillator is a specialized tool designed for long-term mean-reversion analysis of Bitcoin's price relative to a theoretical midline derived from the Bitcoin Power Law model (made by capriole_charles). This oscillator helps investors identify whether Bitcoin is currently overbought, oversold, or near its fair value according to this mathematical model.
Key Features:
Power Law Model Integration: The oscillator is based on the midline of the Bitcoin Power Law, which is calculated using regression coefficients (A and B) applied to the logarithm of the number of days since Bitcoin’s inception. This midline represents a theoretical fair value for Bitcoin over time.
Midline Distance Calculation: The distance between Bitcoin’s current price and the Power Law midline is computed as a percentage, indicating how far above or below the price is from this theoretical value.
float a = input.float (-16.98212206, 'Regression Coef. A', group = "Power Law Settings")
float b = input.float (5.83430649, 'Regression Coef. B', group = "Power Law Settings")
normalization_start_date = timestamp(2011,1,1)
calculation_start_date = time == timestamp(2010, 7, 19, 0, 0) // First BLX Bitcoin Date
int days_since = request.security('BNC:BLX', 'D', ta.barssince(calculation_start_date))
bar() =>
= request.security('BNC:BLX', 'D', bar())
int offset = 564 // days between 2009/1/1 and "calculation_start_date"
int days = days_since + offset
float e = a + b * math.log10(days)
float y = math.pow(10, e)
float midline_distance = math.round((y / btc_close - 1.0) * 100)
Oscillator Normalization: The raw distance is converted into a normalized oscillator, which fluctuates between -1 and 1. This normalization adjusts the oscillator to account for historical extremes, making it easier to compare current conditions with past market behavior.
float oscillator = -midline_distance
var float min = na
var float max = na
if (oscillator > max or na(max)) and time >= normalization_start_date
max := oscillator
if (min > oscillator or na(min)) and time >= normalization_start_date
min := oscillator
rescale(float value, float min, float max) =>
(2 * (value - min) / (max - min)) - 1
normalized_oscillator = rescale(oscillator, min, max)
Overbought/Oversold Identification: The oscillator provides a clear visual representation, where values near 1 suggest Bitcoin is overbought, and values near -1 indicate it is oversold. This can help identify potential reversal points or areas of significant market imbalance.
Optional Moving Average: Users can overlay a moving average (either SMA or EMA) on the oscillator to smooth out short-term fluctuations and focus on longer-term trends. This is particularly useful for confirming trend reversals or persistent overbought/oversold conditions.
This indicator is particularly useful for long-term Bitcoin investors who wish to gauge the market's mean-reversion tendencies based on a well-established theoretical model. By focusing on the Power Law’s midline, users can gain insights into whether Bitcoin’s current price deviates significantly from what historical trends would suggest as a fair value.
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's Logarithmic ChannelLogarithmic growth is a reasonable way to describe the long term growth of bitcoin's market value: for a network that is experiencing growing adoption and is powered by an asset with a finite and disinflationary supply, it’s natural to expect a more explosive growth of its market capitalization early on, followed by diminishing returns as the network and the asset mature.
I used publicly available data to model the market capitalization of bitcoin, deriving thereform a set of three curves forming a logarithmic growth channel for the market capitalization of bitcoin. Using the time series for the circulating supply, we derive a logarithmic growth channel for the bitcoin price.
Model uses publicly available data from July 17, 2010 to December 31, 2022. Everything since the beginning of 2023 is a prediction.
Past performance is not a guarantee of future results.
Short Sale Restriction (SSR) Level - Intraday and daily chartsThis script plots the Short Sale Restriction (SSR) Level relative to the previous day's closing price. It works on any time frame from 1 minute to daily, showing the correct level even during the extended session.
The Short Sale Restriction (SSR) is a rule of the Securities and Exchange Commission (SEC) that restricts traders from short-selling stocks that are rapidly decreasing in value in an attempt to profit from the price drop. The rule was introduced in 2010, after the 2008 financial crisis, to prevent market manipulation and excessive volatility.
The SSR works as follows: when the price of a particular stock drops 10% compared to the previous day's closing price, the SSR is triggered and a temporary limitation is imposed on traders' ability to short-sell that stock for the rest of the trading day and the following day. During the SSR activation period, traders can still short-sell, but only if the sale is "covered" by another long position on the same stock.
Knowledge of the SSR level is especially important for day traders because it helps them to plan their trading strategies in advance, avoiding situations where short-selling becomes more difficult. Additionally, if a stock has exceeded the SSR threshold, traders can expect an increase in price volatility.
RSI SMA Crossover StrategyOverview
RSI SMA Crossover Strategy works the same way as traditional MA crossover strategies, but using RSI instead of price. When RSI crosses over the SMA, a long position is opened (buy). When RSI crosses under the SMA, the long position is closed (sell).
This strategy can be very effective when the right inputs are used (see below). Be sure to use the backtesting tool to determine the optimal parameters for a given asset/timeframe.
Inputs/Parameters
RSI Length: length for RSI calculation (default = 50)
SMA Length: length for SMA calculation (default = 25)
Strategy Properties
Initial Capital = $1000
No default properties are defined for Slippage, Commission, etc, so be sure to set these values to get accurate backtesting results. This script is being published open-source for a reason - save yourself a copy and adjust the settings as you like!
Backtesting Results
Testing on Bitcoin (all time index) 1D chart, with all default parameters.
$1,000 initial investment on 10/07/2010 turns into almost $2.5 billion as of 08/30/2022 (compared to $334 million if the initial investment was held over the same period)
Remember, results can vary greatly based on the variables mentioned above, so always be sure to backtest.
Combo 2/20 EMA & Bandpass Filter This is combo strategies for get a cumulative signal.
First strategy
This indicator plots 2/20 exponential moving average. For the Mov
Avg X 2/20 Indicator, the EMA bar will be painted when the Alert criteria is met.
Second strategy
The related article is copyrighted material from
Stocks & Commodities Mar 2010
WARNING:
- For purpose educate only
- This script to change bars colors.
Overnight Gap AnalysisThere is a wide range of opinion on holding positions overnight due to gap risk. So, out of curiosity, I coded this analysis as a strategy to see what the result of only holding a position overnight on an asset would be. The results really surprised me. The script backtests 10+ years, and here are the findings:
Holding a position for 1 hour bar overnight on QQQ since January 2010 results in a 545% return. QQQ's entire return holding through the same period is 643%
The max equity drawdown on holding that position overnight is lower then the buy/hold drawdown on the underlying asset.
It doesn't matter if the last bar of the day is green or red, the results are similar.
It doesn't matter if it is a bull or bear market. Filtering the script to only trade when the price is above the 200-day moving average actually reduces its return from 545% to 301%, though it does also reduce drawdown.
I see similar patterns when applying the script to other index ETFs. Applying it to leveraged index ETFs can end up beating buy/hold of the underlying index.
Since this script holds through the 1st bar of the day, this could also speak to a day-opening price pattern
The default inputs are for the script to be applied to 1 hour charts only that have 7 bars on the chart per day. You can apply it to other chart types, but must follow the instructions below for it to work properly.
What the script is doing :
This script is buying the close of the last bar of the day and closing the trade at the close of the next bar. So, all trades are being held for 1 bar. By default, the script is setup for use on a 1hr chart that has 7 bars per day. If you try to apply it to a different timeframe, you will need to adjust the count of the last bar of the day with the script input. I.e. There are 7 bars per day on an hour chart on US Stocks/ETFs, so the input is set to 7 by default.
Other ways this script can be used :
This script can also test the result of holding a position over any 1 bar in the day using that same input. For instance, on an hour chart you can input 6 on the script input, and it will model buying the close of the 6th bar of the day while selling on the close of the next bar. I used this out of curiosity to model what only holding the last bar of the day would result in. On average, you lose money on the last bar every day.
The irony here is that the root cause of this last bar of the day losing may be people selling their positions at the end of day so that they aren't exposed to overnight gap risk.
Disclaimer: This is not financial advice. Open-source scripts I publish in the community are largely meant to spark ideas that can be used as building blocks for part of a more robust trade management strategy. If you would like to implement a version of any script, I would recommend making significant additions/modifications to the strategy & risk management functions. If you don’t know how to program in Pine, then hire a Pine-coder. We can help!
Augmented Dickey–Fuller (ADF) mean reversion testThe augmented Dickey-Fuller test (ADF) is a statistical test for the tendency of a price series sample to mean revert .
The current price of a mean-reverting series may tell us something about the next move (as opposed, for example, to a geometric Brownian motion). Thus, the ADF test allows us to spot market inefficiencies and potentially exploit this information in a trading strategy.
Mathematically, the mean reversion property means that the price change in the next time period is proportional to the difference between the average price and the current price. The purpose of the ADF test is to check if this proportionality constant is zero. Accordingly, the ADF test statistic is defined as the estimated proportionality constant divided by the corresponding standard error.
In this script, the ADF test is applied in a rolling window with a user-defined lookback length. The calculated values of the ADF test statistic are plotted as a time series. The more negative the test statistic, the stronger the rejection of the hypothesis that there is no mean reversion. If the calculated test statistic is less than the critical value calculated at a certain confidence level (90%, 95%, or 99%), then the hypothesis of a mean reversion is accepted (strictly speaking, the opposite hypothesis is rejected).
Input parameters:
Source - The source of the time series being tested.
Length - The number of points in the rolling lookback window. The larger sample length makes the ADF test results more reliable.
Maximum lag - The maximum lag included in the test, that defines the order of an autoregressive process being implied in the model. Generally, a non-zero lag allows taking into account the serial correlation of price changes. When dealing with price data, a good starting point is lag 0 or lag 1.
Confidence level - The probability level at which the critical value of the ADF test statistic is calculated. If the test statistic is below the critical value, it is concluded that the sample of the price series is mean-reverting. Confidence level is calculated based on MacKinnon (2010) .
Show Infobox - If True, the results calculated for the last price bar are displayed in a table on the left.
More formal background:
Formally, the ADF test is a test for a unit root in an autoregressive process. The model implemented in this script involves a non-zero constant and zero time trend. The zero lag corresponds to the simple case of the AR(1) process, while higher order autoregressive processes AR(p) can be approached by setting the maximum lag of p. The null hypothesis is that there is a unit root, with the alternative that there is no unit root. The presence of unit roots in an autoregressive time series is characteristic for a non-stationary process. Thus, if there is no unit root, the time series sample can be concluded to be stationary, i.e., manifesting the mean-reverting property.
A few more comments:
It should be noted that the ADF test tells us only about the properties of the price series now and in the past. It does not directly say whether the mean-reverting behavior will retain in the future.
The ADF test results don't directly reveal the direction of the next price move. It only tells wether or not a mean-reverting trading strategy can be potentially applicable at the given moment of time.
The ADF test is related to another statistical test, the Hurst exponent. The latter is available on TradingView as implemented by balipour , QuantNomad and DonovanWall .
The ADF test statistics is a negative number. However, it can take positive values, which usually corresponds to trending markets (even though there is no statistical test for this case).
Rigorously, the hypothesis about the mean reversion is accepted at a given confidence level when the value of the test statistic is below the critical value. However, for practical trading applications, the values which are low enough - but still a bit higher than the critical one - can be still used in making decisions.
Examples:
The VIX volatility index is known to exhibit mean reversion properties (volatility spikes tend to fade out quickly). Accordingly, the statistics of the ADF test tend to stay below the critical value of 90% for long time periods.
The opposite case is presented by BTCUSD. During the same time range, the bitcoin price showed strong momentum - the moves away from the mean did not follow by the counter-move immediately, even vice versa. This is reflected by the ADF test statistic that consistently stayed above the critical value (and even above 0). Thus, using a mean reversion strategy would likely lead to losses.
MathConstantsAtomicLibrary "MathConstantsAtomic"
Mathematical Constants
FineStructureConstant() Fine Structure Constant: alpha = e^2/4*Pi*e_0*h_bar*c_0 (2007 CODATA)
RydbergConstant() Rydberg Constant: R_infty = alpha^2*m_e*c_0/2*h (2007 CODATA)
BohrRadius() Bor Radius: a_0 = alpha/4*Pi*R_infty (2007 CODATA)
HartreeEnergy() Hartree Energy: E_h = 2*R_infty*h*c_0 (2007 CODATA)
QuantumOfCirculation() Quantum of Circulation: h/2*m_e (2007 CODATA)
FermiCouplingConstant() Fermi Coupling Constant: G_F/(h_bar*c_0)^3 (2007 CODATA)
WeakMixingAngle() Weak Mixin Angle: sin^2(theta_W) (2007 CODATA)
ElectronMass() Electron Mass: (2007 CODATA)
ElectronMassEnergyEquivalent() Electron Mass Energy Equivalent: (2007 CODATA)
ElectronMolarMass() Electron Molar Mass: (2007 CODATA)
ComptonWavelength() Electron Compton Wavelength: (2007 CODATA)
ClassicalElectronRadius() Classical Electron Radius: (2007 CODATA)
ThomsonCrossSection() Thomson Cross Section: (2002 CODATA)
ElectronMagneticMoment() Electron Magnetic Moment: (2007 CODATA)
ElectronGFactor() Electon G-Factor: (2007 CODATA)
MuonMass() Muon Mass: (2007 CODATA)
MuonMassEnegryEquivalent() Muon Mass Energy Equivalent: (2007 CODATA)
MuonMolarMass() Muon Molar Mass: (2007 CODATA)
MuonComptonWavelength() Muon Compton Wavelength: (2007 CODATA)
MuonMagneticMoment() Muon Magnetic Moment: (2007 CODATA)
MuonGFactor() Muon G-Factor: (2007 CODATA)
TauMass() Tau Mass: (2007 CODATA)
TauMassEnergyEquivalent() Tau Mass Energy Equivalent: (2007 CODATA)
TauMolarMass() Tau Molar Mass: (2007 CODATA)
TauComptonWavelength() Tau Compton Wavelength: (2007 CODATA)
ProtonMass() Proton Mass: (2007 CODATA)
ProtonMassEnergyEquivalent() Proton Mass Energy Equivalent: (2007 CODATA)
ProtonMolarMass() Proton Molar Mass: (2007 CODATA)
ProtonComptonWavelength() Proton Compton Wavelength: (2007 CODATA)
ProtonMagneticMoment() Proton Magnetic Moment: (2007 CODATA)
ProtonGFactor() Proton G-Factor: (2007 CODATA)
ShieldedProtonMagneticMoment() Proton Shielded Magnetic Moment: (2007 CODATA)
ProtonGyromagneticRatio() Proton Gyro-Magnetic Ratio: (2007 CODATA)
ShieldedProtonGyromagneticRatio() Proton Shielded Gyro-Magnetic Ratio: (2007 CODATA)
NeutronMass() Neutron Mass: (2007 CODATA)
NeutronMassEnegryEquivalent() Neutron Mass Energy Equivalent: (2007 CODATA)
NeutronMolarMass() Neutron Molar Mass: (2007 CODATA)
NeutronComptonWavelength() Neuron Compton Wavelength: (2007 CODATA)
NeutronMagneticMoment() Neutron Magnetic Moment: (2007 CODATA)
NeutronGFactor() Neutron G-Factor: (2007 CODATA)
NeutronGyromagneticRatio() Neutron Gyro-Magnetic Ratio: (2007 CODATA)
DeuteronMass() Deuteron Mass: (2007 CODATA)
DeuteronMassEnegryEquivalent() Deuteron Mass Energy Equivalent: (2007 CODATA)
DeuteronMolarMass() Deuteron Molar Mass: (2007 CODATA)
DeuteronMagneticMoment() Deuteron Magnetic Moment: (2007 CODATA)
HelionMass() Helion Mass: (2007 CODATA)
HelionMassEnegryEquivalent() Helion Mass Energy Equivalent: (2007 CODATA)
HelionMolarMass() Helion Molar Mass: (2007 CODATA)
Avogadro() Avogadro constant: (2010 CODATA)
Financial Astrology Juno LongitudeJuno is the 4th largest object in terms of mass in the asteroid belt between Mars and Jupiter, this asteroid is not widely used by financial astrologers but as was demonstrated in our research with Ceres and Vesta, the objects in the asteroid belt seems to be very important for the trend forecast. The zodiacal energy of this objects cannot be ignored for an accurate analysis. Based in BTCUSD historical price data we calculated the daily trend (buy/sell) during the periods where Juno was transiting across different zodiac signs and we found some significant patterns:
INDEX:BTCUSD
Bullish zodiac signs
From 387 days located in Scorpio, price increased 62% of the days.
From 316 days located in Capricorn, price increased 64% of the days.
From 300 days located in Sagittarius, price increased 56% of the days.
From 435 days located in Libra, price increased 55% of the days.
Bearish zodiac signs
From 200 days located in Taurus, price decreased 56% of the days.
From 152 days located in Virgo, price decreased 58% of the days.
Note: The Juno longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Random Entries Work!" tHe MaRkEtS aRe RaNdOm ", say moron academics.
The purpose of this study is to show that most markets are NOT random! Most markets show a clear bias where we can make such easy money, that a random number generator can do it.
=== HOW THE INDICATOR WORKS ===
The study will randomly enter the market
The study will randomly exit the market if in a trade
You can choose a Long Only, Short Only, or Bidirectional strategy
=== DEFAULT VALUES AND THEIR LOGIC ===
Percent Chance to Enter Per Bar: 10%
Percent Chance to Exit Per Bar: 3%
Direction: Long Only
Commission: 0
Each bar has a 10% chance to enter the market. Each bar has a 3% to exit the market . It will only enter long.
I included zero commission for simplification. It's a good exercise to include a commission/slippage to see just how much trading fees take from you.
=== TIPS ===
Increasing "Percent Chance to Exit" will shorten the time in a trade. You can see the "Avg # Bars In Trade" go down as you increase. If "Percent Chance to Exit" is too high, the study won't be in the market long enough to catch any movement, possibly exiting on the same bar most of the time.
If you're getting the red screen, that means the strategy lost so much money it went broke. Try reducing the percent equity on the Properties tab.
Switch the start year to avoid/minimize black swan events like the covid drop in 2020.
=== FINDINGS ===
Most markets lose money with a "Random" direction strategy.
Most markets lose ALL money with a "Short Only" strategy.
Most markets make money with a "Long Only" strategy.
Try this strategy on: Bitcoin (BTCUSD) and the NASDAQ (QQQ).
There are two popular memes right now: "Bitcoin to the moon" and "Stocks only go up". Both are seemingly true. Bitcoin was the best performing asset of the 2010's, gaining several billion percent in gains. The stock market is on a 100 year long uptrend. Why? BECAUSE FIAT CURRENCIES ALWAYS GO DOWN! This is inflation. If we measure the market in terms of others assets instead of fiat, the Long Only strategy doesn't work anymore (or works less well).
Try this strategy on: Bitcoin/GLD (BTCUSD/GLD), the Eurodollar (EURUSD), and the S&P 500 measured in gold (SPY/GLD).
Bitcoin measured in gold (BTCUSD/GLD) still works with a Long Only strategy because Bitcoin increased in value over both USD and gold.
The Eurodollar (EURUSD) generally loses money no matter what, especially if you add any commission. This makes sense as they are both fiat currencies with similar inflation schedules.
Gold and the S&P 500 have gained roughly the same amount since ~2000. Some years will show better results for a long strategy, while others will favor a short strategy. Now look at just SPY or GLD (which are both measured in USD by default!) and you'll see the same trend again: a Long Only strategy crushes even when entering and exiting randomly.
=== " JUST TELL ME WHAT TO DO, YOU NERD! " ===
Bulls always win and Bears always lose because fiat currencies go to zero.
You're not underperforming a random number generator, are you?
Financial Astrology Vesta SpeedVesta (asteroid) speed provides a good indicator to determine the periods of dominant trend. During the direct phase (when the speed accelerated and reached highest value) we can observe that BTCUSD experienced a clear trend, perfect for trend following. In the contrary when speed was decelerating and speed started backward motion (retrograde) the price was in congestion experiencing sideways moves. From statistical analysis we noted that when Vesta speed is in direct motion 56% of the days resulted in price increase. When speed was stationary (starting to move retrograde) we observed that in 62% of the days the price decreased, finally, during retrograde phase in 54% of the days the price increased. Is clear that direct motion also offers more bullish days. However, in the statistical analysis of the price is not evident the price change range, with visual exploration in the chart is clear that when Vesta speed is in direct phase the range of the price is wider, therefore, direct motion provides the most interesting risk/reward ratio.
Note: The Vesta speed indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Financial Astrology Vesta DeclinationVesta (asteroid) declination show a strong correlation with the BTCUSD trend, we can clearly see that all the most intense bullish periods have occurred when declination was moving from South to Node direction (when the slope is positive). In the events when declination was moving toward North and have penetrated the zero declination boundary (horizontal dashed line) we can observe a periods where price experienced more volatility.
Note: The Vesta declination indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Financial Astrology Vesta LongitudeVesta is one of the largest objects in the asteroid belt between Mars and Jupiter, the orbit duration is 3.63 years and seems to be very relevant celestial object in financial astrology. The experienced financial astrologer "Bill Meridian" indicates that this asteroid rules the security business, and paper securities such as bonds and stocks. We have confirmed through statistical research that adding this asteroid to astrology machine learning models provides an increase in daily trend predictions accuracy for crypto-currencies sector.
Our statistical analysis of Vesta zodiac sign location concluded that when is transiting the signs of Aries, Gemini, Cancer, Leo and Libra the daily trend is 59% or more of the days bullish. When Vesta is located at Capricorn is very bearish with 60% of the daily trend going in downward direction. In the other zodiac signs the daily trend was neutral showing most of the time a sideways pattern.
Is very interesting to note that the exact date July 21, 2021, when Vesta entered in Libra BTCUSD started the last bullish wave that finally broke the congestion zone of the 30K-35K and started a new bullish optimism. Pay attention on what happened in the previous cycle when Vesta was located in Libra and do your conclusions.
Note: Vesta longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Financial Astrology True Lilith (Black Moon) LongitudeTrue Lilith (Black Moon) represents the wildly perturbed Moon apogee orbit, is not averaged (as Mean Lilith) and shows an erratic path with constant change of direction and speed. This Lilith uses the actual, real orbit rather than the average used by Mean Lilith. This perturbations are caused due to the gravitational pull of the Sun and the change of the orbit center which is the Earth-Moon Barycenter. The move of this apogee point toward all the Zodiac signs takes around 9 years to complete and as we can observe, the True Lilith moves back and forward within two consecutive zodiac signs during a prolonged period. In this erratic motion we can note that the peaks and valleys of this waves usually present a swing trade opportunities, is really impressive to note how a full or half True Lilith wave period correlates with short term local peaks and valleys in the BTCUSD price.
Note: The True Lilith (Black Moon) longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Financial Astrology Mean Lilith (Black Moon) LongitudeMean Lilith (Black Moon) represents the apogee of the lunar orbit (point where the Moon is farthest from Earth) as the Moon experience perturbations due to the gravitational pull of the Sun and don't orbit in elliptical path due the fact that don't follow the Earth center but the Earth-Moon Barycenter cause that an average projection of this apogee point location needs to be calculated, for this reason, we need to differentiate the Mean Lilith and True Lilith. The move of this apogee point toward all the Zodiac signs takes around 9 years to complete so in BTCUSD asset we only have one complete revolution so is difficult to emit any clear judgement of the zodiac sign location influence in the trend. However this imaginary body named Lilith is widely adopted by astrologers and is very important in Chinese Astrology, for this reason, we decided to contribute the indicator to support the research of Chinese astro-traders.
Note: The Mean Lilith (Black Moon) longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
Financial Astrology South Node (Ketu) DeclinationThe declination of South Node (Ketu) is the inverse of North Node (Rahu), therefore, the only relevant pattern that we detected is that when declination was within -6 to +6 degrees the price was congested within narrow price zone as was previously mentioned at the North Node (Rahu) declination indicator.
Note: The South Node (Ketu) declination indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the data is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart timezone.
