Maths — 指標和策略

Correlation Heatmap Matrix [TradingFinder] 20 Assets Variable 🔵 Introduction Correlation is one of the most important statistical and analytical metrics in financial markets, data mining, and data science. It measures the strength and direction of the relationship between two variables. The correlation coefficient always ranges between +1 and -1 : a perfect positive correlation (+1) means that two assets or currency pairs move together in the same direction and at a constant ratio, a correlation of zero (0) indicates no clear linear relationship, and a perfect negative correlation (-1) means they move in exactly opposite directions. While the Pearson Correlation Coefficient is the most common method for calculation, other statistical methods like Spearman and Kendall are also used depending on the context. In financial market analysis, correlation is a key tool for Forex, the Stock Market, and the Cryptocurrency Market because it allows traders to assess the price relationship between currency pairs, stocks, or coins. For example, in Forex, EUR/USD and GBP/USD often have a high positive correlation; in stocks, companies from the same sector such as Apple and Microsoft tend to move similarly; and in crypto, most altcoins show a strong positive correlation with Bitcoin. Using a Correlation Heatmap in these markets visually displays the strength and direction of these relationships, helping traders make more accurate decisions for risk management and strategy optimization. 🟣 Correlation in Financial Markets In finance, correlation refers to measuring how closely two assets move together over time. These assets can be stocks, currency pairs, commodities, indices, or cryptocurrencies. The main goal of correlation analysis in trading is to understand these movement patterns and use them for risk management, trend forecasting, and developing trading strategies. 🟣 Correlation Heatmap A correlation heatmap is a visual tool that presents the correlation between multiple assets in a color-coded table. Each cell shows the correlation coefficient between two assets, with colors indicating its strength and direction. Warm colors (such as red or orange) represent strong negative correlation, cool colors (such as blue or cyan) represent strong positive correlation, and mid-range tones (such as yellow or green) indicate correlations that are close to neutral. 🟣 Practical Applications in Markets Forex : Identify currency pairs that move together or in opposite directions, avoid overexposure to similar trades, and spot unusual divergences. Crypto : Examine the dependency of altcoins on Bitcoin and find independent movers for portfolio diversification. Stocks : Detect relationships between stocks in the same industry or find outliers that move differently from their sector. 🟣 Key Uses of Correlation in Trading Risk management and diversification: Select assets with low or negative correlation to reduce portfolio volatility. Avoiding overexposure: Prevent opening multiple positions on highly correlated assets. Pairs trading: Exploit temporary deviations between historically correlated assets for arbitrage opportunities. Intermarket analysis: Study the relationships between different markets like stocks, currencies, commodities, and bonds. Divergence detection: Spot when two typically correlated assets move apart as a possible trend change signal. Market forecasting: Use correlated asset movements to anticipate others’ behavior. Event reaction analysis: Evaluate how groups of assets respond to economic or political events. ❗ Important Note It’s important to note that correlation does not imply causation — it only reflects co-movement between assets. Correlation is also dynamic and can change over time, which is why analyzing it across multiple timeframes provides a more accurate picture. Combining correlation heatmaps with other analytical tools can significantly improve the precision of trading decisions. 🔵 How to Use The Correlation Heatmap Matrix indicator is designed to analyze and manage the relationships between multiple assets at once. After adding the tool to your chart, start by selecting the assets you want to compare (up to 20). Then, choose the Correlation Period that fits your trading strategy. Shorter periods (e.g., 20 bars) are more sensitive to recent price movements, making them suitable for short-term trading, while longer periods (e.g., 100 or 200 bars) provide a broader view of correlation trends over time. The indicator outputs a color-coded matrix where each cell represents the correlation between two assets. Warm colors like red and orange signal strong negative correlation, while cool colors like blue and cyan indicate strong positive correlation. Mid-range tones such as yellow or green suggest correlations that are close to neutral. This visual representation makes it easy to spot market patterns at a glance. One of the most valuable uses of this tool is in portfolio risk management. Portfolios with highly correlated assets are more vulnerable to market swings. By using the heatmap, traders can find assets with low or negative correlation to reduce overall risk. Another key benefit is preventing overexposure. For example, if EUR/USD and GBP/USD have a high positive correlation, opening trades on both is almost like doubling the position size on one asset, increasing risk unnecessarily. The heatmap makes such relationships clear, helping you avoid them. The indicator is also useful for pairs trading, where a trader identifies assets that are usually correlated but have temporarily diverged — a potential arbitrage or mean-reversion opportunity. Additionally, the tool supports intermarket analysis, allowing traders to see how movements in one market (e.g., crude oil) may impact others (e.g., the Canadian dollar). Divergence detection is another advantage: if two typically aligned assets suddenly move in opposite directions, it could signal a major trend shift or a news-driven move. Overall, the Correlation Heatmap Matrix is not just an analytical indicator but also a fast, visual alert system for monitoring multiple markets at once. This is particularly valuable for traders in fast-moving environments like Forex and crypto. 🔵 Settings 🟣 Logic Correlation Period : Number of bars used to calculate correlation between assets. 🟣 Display Table on Chart : Enable/disable displaying the heatmap directly on the chart. Table Size : Choose the table size (from very small to very large). Table Position : Set the table location on the chart (top, middle, or bottom in various alignments). 🟣 Symbol Custom Select Market : Choose the market type (Forex, Stocks, Crypto, or Custom). Symbol 1 to Symbol 20: In custom mode, you can define up to 20 assets for correlation calculation. 🔵 Conclusion The Correlation Heatmap Matrix is a powerful tool for analyzing correlations across multiple assets in Forex, crypto, and stock markets. By displaying a color-coded table, it visually conveys both the strength and direction of correlations — warm colors for strong negative correlation, cool colors for strong positive correlation, and mid-range tones such as yellow or green for near-zero or neutral correlation. This helps traders select assets with low or negative correlation for diversification, avoid overexposure to similar trades, identify arbitrage and pairs trading opportunities, and detect unusual divergences between typically aligned assets. With support for custom mode and up to 20 symbols, it offers high flexibility for different trading strategies, making it a valuable complement to technical analysis and risk management.

MathHelpers Library "MathHelpers" Overview A collection of helper functions for designing indicators and strategies. calculateATR(length, log) Calculates the Average True Range (ATR) or Log ATR based on the 'log' parameter. Sans Wilder's Smoothing Parameters: length (simple int) log (simple bool) Returns: float The calculated ATR value. Returns Log ATR if `log` is true, otherwise returns standard ATR. CDF(z) Computes the Cumulative Distribution Function (CDF) for a given value 'z', mimicking the CDF function in "Statistically Sound Indicators" by Timothy Masters. Parameters: z (simple float) Returns: float The CDF value corresponding to the input `z`, ranging between 0 and 1. logReturns(lookback) Calculates the logarithmic returns over a specified lookback period. Parameters: lookback (simple int) Returns: float The calculated logarithmic return. Returns `na` if insufficient data is available.

Weierstrass Function (Fractal Cycles)THE WEIERSTRASS FUNCTION f(x) = ∑(n=0)^∞ a^n * cos(b^n * π * x) The Weierstrass Function is the sum of an infinite series of cosine functions, each with increasing frequency and decreasing amplitude. This creates powerful multi-scale oscillations within the range ⬍(-2;+2), resembling a system of self-repetitive patterns. You can zoom into any part of the output and observe similar proportions, mimicking the hidden order behind the irregularity and unpredictability of financial markets. IT DOESN’T RELY ON ANY MARKET DATA, AS THE OUTPUT IS BASED PURELY ON A MATHEMATICAL FORMULA! This script does not provide direct buy or sell signals and should be used as a tool for analyzing the market behavior through fractal geometry. The function is often used to model complex, chaotic systems, including natural phenomena and financial markets. APPLICATIONS: Timing Aspect: Identifies the phases of market cycles, helping to keep awareness of frequency of turning points Price-Modeling features: The Amplitude, frequency, and scaling settings allow the indicator to simulate the trends and oscillations. Its nowhere-differentiable nature aligns with the market's inherent uncertainty. The fractured oscillations resemble sharp jumps, noise, and dips found in volatile markets. SETTINGS Amplitude Factor (a): Controls the size of each wave. A higher value makes the waves larger. Frequency Factor (b): Determines how fast the waves oscillate. A higher value creates more frequent waves. Ability to Invert the output: Just like any cosine function it starts its journey with a decline, which is not distinctive to the behavior of most assets. The default setting is in "inverted mode". Scale Factor: Adjusts the speed at which the oscillations grow over time. Number of Terms (n_terms): Increases the number of waves. More terms add complexity to the pattern.

Guassian Distribution Forecast [prediction intervals]The Indicator The Indicator combines volatility and frequency distributions to forecast an area of possible price expansion with an approximate confidence interval / level and level of significance (significance level). The Script Formula Additional comments To alter the models forecasting precision to reflect a given confidence interval, e.g the 90% confidence level (C.L.), use the 1.64 multiplier (toggle value in "Standard normal distribution sd" setting), to use a specific C.L., e.g. the 85th percentile either search for this on google, or calculate it yourself using a Standard Normal Distribution Probability table. Additionaly volatility may be changed by toggling the lookback period setting, this can be thought of as widening the distribution tails. The look forward parameter is currently fixed at 20, this is because it does not currently work correctly with higher integers, I will try resolve this problem and any other bugs as soon as possible

Autocorrelation - The Quant Science Autocorrelation - The Quant Science it is an indicator developed to quickly calculate the autocorrelation of a historical series. The objective of this indicator is to plot the autocorrelation values and highlight market moments where the value is positive and exceeds the attention threshold. This indicator can be used for manual analysis when a trader needs to search for new price patterns within the historical series or to create complex formulas in estimating future prices. What is autocorrelation? Autocorrelation in trading is a statistical measure used to determine the presence of a relationship or pattern of dependence between values in a financial time series over time. It represents the correlation of past values in a series with its future values. In other words, autocorrelation in trading aims to identify if there are systematic relationships between the past prices or returns of a security or market and its future prices or returns. This analysis can be helpful in identifying patterns or trends that can be leveraged for informed trading decisions. The presence of autocorrelation may suggest that market prices or returns follow a certain pattern or trend over time. Limitations of the model It is important to note that autocorrelation does not necessarily imply a causal relationship between past and future values. Other variables or market factors may influence the dynamics of prices or returns, and therefore autocorrelation could be merely a random coincidence. Therefore, it is essential to carefully evaluate the results of autocorrelation analysis along with other information and trading strategies to make informed decisions. How to use The usage is very simple, you just need to add it to the current chart to activate the indicator. From the user interface, you can manage two important features: 1. Lenght: the delay period applied to the historical series during the autocorrelation calculation can be managed from the user interface. By default, it is set to 20, which means that the autocorrelation ratio within the historical series is calculated with a delay of 20 bars. 2. Threshold: the threshold value that the autocorrelation level must meet can be managed from the user interface. By default, it is set to 0.50, which means that the autocorrelation value must be higher than this threshold to be considered valid and displayed on the chart. 3. Bar color: the color used to display the autocorrelation data and highlight the bars when autocorrelation is valid can be managed from the user interface. To set up the chart We recommend disabling the 'wick' and 'border' of the candlesticks from the chart settings for a high-quality user experience.

Source Correlation In this small indicator I make it possible for the user to set two different input sources. Then, the indicator displays the correlation of these two input sources. It's a very small script, but I think it could be helpful to somebody to find uncorrelated indicators for his trading strategy. To use uncorrelated indicators is in general recommended. Enjoy this small, but powerful tool. 🧙‍♂️