Scientific Correlation Testing FrameworkScientific Correlation Testing Framework - Comprehensive Guide
Introduction to Correlation Analysis
What is Correlation?
Correlation is a statistical measure that describes the degree to which two assets move in relation to each other. Think of it like measuring how closely two dancers move together on a dance floor.
Perfect Positive Correlation (+1.0): Both dancers move in perfect sync, same direction, same speed
Perfect Negative Correlation (-1.0): Both dancers move in perfect sync but in opposite directions
Zero Correlation (0): The dancers move completely independently of each other
In financial markets, correlation helps us understand relationships between different assets, which is crucial for:
Portfolio diversification
Risk management
Pairs trading strategies
Hedging positions
Market analysis
Why This Script is Special
This script goes beyond simple correlation calculations by providing:
Two different correlation methods (Pearson and Spearman)
Statistical significance testing to ensure results are meaningful
Rolling correlation analysis to track how relationships change over time
Visual representation for easy interpretation
Comprehensive statistics table with detailed metrics
Deep Dive into the Script's Components
1. Input Parameters Explained-
Symbol Selection:
This allows you to select the second asset to compare with the chart's primary asset
Default is Apple (NASDAQ:AAPL), but you can change this to any symbol
Example: If you're viewing a Bitcoin chart, you might set this to "NASDAQ:TSLA" to see if Bitcoin and Tesla are correlated
Correlation Window (60): This is the number of periods used to calculate the main correlation
Larger values (e.g., 100-500) provide more stable, long-term correlation measures
Smaller values (e.g., 10-50) are more responsive to recent price movements
60 is a good balance for most daily charts (about 3 months of trading days)
Rolling Correlation Window (20): A shorter window to detect recent changes in correlation
This helps identify when the relationship between assets is strengthening or weakening
Default of 20 is roughly one month of trading days
Return Type: This determines how price changes are calculated
Simple Returns: (Today's Price - Yesterday's Price) / Yesterday's Price
Easy to understand: "The asset went up 2% today"
Log Returns: Natural logarithm of (Today's Price / Yesterday's Price)
More mathematically elegant for statistical analysis
Better for time-additive properties (returns over multiple periods)
Less sensitive to extreme values.
Confidence Level (95%): This determines how certain we want to be about our results
95% confidence means we accept a 5% chance of being wrong (false positive)
Higher confidence (e.g., 99%) makes the test more strict
Lower confidence (e.g., 90%) makes the test more lenient
95% is the standard in most scientific research
Show Statistical Significance: When enabled, the script will test if the correlation is statistically significant or just due to random chance.
Display options control what you see on the chart:
Show Pearson/Spearman/Rolling Correlation: Toggle each correlation type on/off
Show Scatter Plot: Displays a scatter plot of returns (limited to recent points to avoid performance issues)
Show Statistical Tests: Enables the detailed statistics table
Table Text Size: Adjusts the size of text in the statistics table
2.Functions explained-
calcReturns():
This function calculates price returns based on your selected method:
Log Returns:
Formula: ln(Price_t / Price_t-1)
Example: If a stock goes from $100 to $101, the log return is ln(101/100) = ln(1.01) ≈ 0.00995 or 0.995%
Benefits: More symmetric, time-additive, and better for statistical modeling
Simple Returns:
Formula: (Price_t - Price_t-1) / Price_t-1
Example: If a stock goes from $100 to $101, the simple return is (101-100)/100 = 0.01 or 1%
Benefits: More intuitive and easier to understand
rankArray():
This function calculates the rank of each value in an array, which is used for Spearman correlation:
How ranking works:
The smallest value gets rank 1
The second smallest gets rank 2, and so on
For ties (equal values), they get the average of their ranks
Example: For values
Sorted:
Ranks: (the two 2s tie for ranks 1 and 2, so they both get 1.5)
Why this matters: Spearman correlation uses ranks instead of actual values, making it less sensitive to outliers and non-linear relationships.
pearsonCorr():
This function calculates the Pearson correlation coefficient:
Mathematical Formula:
r = (nΣxy - ΣxΣy) / √
Where x and y are the two variables, and n is the sample size
What it measures:
The strength and direction of the linear relationship between two variables
Values range from -1 (perfect negative linear relationship) to +1 (perfect positive linear relationship)
0 indicates no linear relationship
Example:
If two stocks have a Pearson correlation of 0.8, they have a strong positive linear relationship
When one stock goes up, the other tends to go up in a fairly consistent proportion
spearmanCorr():
This function calculates the Spearman rank correlation:
How it works:
Convert each value in both datasets to its rank
Calculate the Pearson correlation on the ranks instead of the original values
What it measures:
The strength and direction of the monotonic relationship between two variables
A monotonic relationship is one where as one variable increases, the other either consistently increases or decreases
It doesn't require the relationship to be linear
When to use it instead of Pearson:
When the relationship is monotonic but not linear
When there are significant outliers in the data
When the data is ordinal (ranked) rather than interval/ratio
Example:
If two stocks have a Spearman correlation of 0.7, they have a strong positive monotonic relationship
When one stock goes up, the other tends to go up, but not necessarily in a straight-line relationship
tStatistic():
This function calculates the t-statistic for correlation:
Mathematical Formula: t = r × √((n-2)/(1-r²))
Where r is the correlation coefficient and n is the sample size
What it measures:
How many standard errors the correlation is away from zero
Used to test the null hypothesis that the true correlation is zero
Interpretation:
Larger absolute t-values indicate stronger evidence against the null hypothesis
Generally, a t-value greater than 2 (in absolute terms) is considered statistically significant at the 95% confidence level
criticalT() and pValue():
These functions provide approximations for statistical significance testing:
criticalT():
Returns the critical t-value for a given degrees of freedom (df) and significance level
The critical value is the threshold that the t-statistic must exceed to be considered statistically significant
Uses approximations since Pine Script doesn't have built-in statistical distribution functions
pValue():
Estimates the p-value for a given t-statistic and degrees of freedom
The p-value is the probability of observing a correlation as strong as the one calculated, assuming the true correlation is zero
Smaller p-values indicate stronger evidence against the null hypothesis
Standard interpretation:
p < 0.01: Very strong evidence (marked with **)
p < 0.05: Strong evidence (marked with *)
p ≥ 0.05: Weak evidence, not statistically significant
stdev():
This function calculates the standard deviation of a dataset:
Mathematical Formula: σ = √(Σ(x-μ)²/(n-1))
Where x is each value, μ is the mean, and n is the sample size
What it measures:
The amount of variation or dispersion in a set of values
A low standard deviation indicates that the values tend to be close to the mean
A high standard deviation indicates that the values are spread out over a wider range
Why it matters for correlation:
Standard deviation is used in calculating the correlation coefficient
It also provides information about the volatility of each asset's returns
Comparing standard deviations helps understand the relative riskiness of the two assets.
3.Getting Price Data-
price1: The closing price of the primary asset (the chart you're viewing)
price2: The closing price of the secondary asset (the one you selected in the input parameters)
Returns are used instead of raw prices because:
Returns are typically stationary (mean and variance stay constant over time)
Returns normalize for price levels, allowing comparison between assets of different values
Returns represent what investors actually care about: percentage changes in value
4.Information Table-
Creates a table to display statistics
Only shows on the last bar to avoid performance issues
Positioned in the top right of the chart
Has 2 columns and 15 rows
Populating the Table
The script then populates the table with various statistics:
Header Row: "Metric" and "Value"
Sample Information: Sample size and return type
Pearson Correlation: Value, t-statistic, p-value, and significance
Spearman Correlation: Value, t-statistic, p-value, and significance
Rolling Correlation: Current value
Standard Deviations: For both assets
Interpretation: Text description of the correlation strength
The table uses color coding to highlight important information:
Green for significant positive results
Red for significant negative results
Yellow for borderline significance
Color-coded headers for each section
=> Practical Applications and Interpretation
How to Interpret the Results
Correlation Strength
0.0 to 0.3 (or 0.0 to -0.3): Weak or no correlation
The assets move mostly independently of each other
Good for diversification purposes
0.3 to 0.7 (or -0.3 to -0.7): Moderate correlation
The assets show some tendency to move together (or in opposite directions)
May be useful for certain trading strategies but not extremely reliable
0.7 to 1.0 (or -0.7 to -1.0): Strong correlation
The assets show a strong tendency to move together (or in opposite directions)
Can be useful for pairs trading, hedging, or as a market indicator
Statistical Significance
p < 0.01: Very strong evidence that the correlation is real
Marked with ** in the table
Very unlikely to be due to random chance
p < 0.05: Strong evidence that the correlation is real
Marked with * in the table
Unlikely to be due to random chance
p ≥ 0.05: Weak evidence that the correlation is real
Not marked in the table
Could easily be due to random chance
Rolling Correlation
The rolling correlation shows how the relationship between assets changes over time
If the rolling correlation is much different from the long-term correlation, it suggests the relationship is changing
This can indicate:
A shift in market regime
Changing fundamentals of one or both assets
Temporary market dislocations that might present trading opportunities
Trading Applications
1. Portfolio Diversification
Goal: Reduce overall portfolio risk by combining assets that don't move together
Strategy: Look for assets with low or negative correlations
Example: If you hold tech stocks, you might add some utilities or bonds that have low correlation with tech
2. Pairs Trading
Goal: Profit from the relative price movements of two correlated assets
Strategy:
Find two assets with strong historical correlation
When their prices diverge (one goes up while the other goes down)
Buy the underperforming asset and short the outperforming asset
Close the positions when they converge back to their normal relationship
Example: If Coca-Cola and Pepsi are highly correlated but Coca-Cola drops while Pepsi rises, you might buy Coca-Cola and short Pepsi
3. Hedging
Goal: Reduce risk by taking an offsetting position in a negatively correlated asset
Strategy: Find assets that tend to move in opposite directions
Example: If you hold a portfolio of stocks, you might buy some gold or government bonds that tend to rise when stocks fall
4. Market Analysis
Goal: Understand market dynamics and interrelationships
Strategy: Analyze correlations between different sectors or asset classes
Example:
If tech stocks and semiconductor stocks are highly correlated, movements in one might predict movements in the other
If the correlation between stocks and bonds changes, it might signal a shift in market expectations
5. Risk Management
Goal: Understand and manage portfolio risk
Strategy: Monitor correlations to identify when diversification benefits might be breaking down
Example: During market crises, many assets that normally have low correlations can become highly correlated (correlation convergence), reducing diversification benefits
Advanced Interpretation and Caveats
Correlation vs. Causation
Important Note: Correlation does not imply causation
Example: Ice cream sales and drowning incidents are correlated (both increase in summer), but one doesn't cause the other
Implication: Just because two assets move together doesn't mean one causes the other to move
Solution: Look for fundamental economic reasons why assets might be correlated
Non-Stationary Correlations
Problem: Correlations between assets can change over time
Causes:
Changing market conditions
Shifts in monetary policy
Structural changes in the economy
Changes in the underlying businesses
Solution: Use rolling correlations to monitor how relationships change over time
Outliers and Extreme Events
Problem: Extreme market events can distort correlation measurements
Example: During a market crash, many assets may move in the same direction regardless of their normal relationship
Solution:
Use Spearman correlation, which is less sensitive to outliers
Be cautious when interpreting correlations during extreme market conditions
Sample Size Considerations
Problem: Small sample sizes can produce unreliable correlation estimates
Rule of Thumb: Use at least 30 data points for a rough estimate, 60+ for more reliable results
Solution:
Use the default correlation length of 60 or higher
Be skeptical of correlations calculated with small samples
Timeframe Considerations
Problem: Correlations can vary across different timeframes
Example: Two assets might be positively correlated on a daily basis but negatively correlated on a weekly basis
Solution:
Test correlations on multiple timeframes
Use the timeframe that matches your trading horizon
Look-Ahead Bias
Problem: Using information that wouldn't have been available at the time of trading
Example: Calculating correlation using future data
Solution: This script avoids look-ahead bias by using only historical data
Best Practices for Using This Script
1. Appropriate Parameter Selection
Correlation Window:
For short-term trading: 20-50 periods
For medium-term analysis: 50-100 periods
For long-term analysis: 100-500 periods
Rolling Window:
Should be shorter than the main correlation window
Typically 1/3 to 1/2 of the main window
Return Type:
For most applications: Log Returns (better statistical properties)
For simplicity: Simple Returns (easier to interpret)
2. Validation and Testing
Out-of-Sample Testing:
Calculate correlations on one time period
Test if they hold in a different time period
Multiple Timeframes:
Check if correlations are consistent across different timeframes
Economic Rationale:
Ensure there's a logical reason why assets should be correlated
3. Monitoring and Maintenance
Regular Review:
Correlations can change, so review them regularly
Alerts:
Set up alerts for significant correlation changes
Documentation:
Keep notes on why certain assets are correlated and what might change that relationship
4. Integration with Other Analysis
Fundamental Analysis:
Combine correlation analysis with fundamental factors
Technical Analysis:
Use correlation analysis alongside technical indicators
Market Context:
Consider how market conditions might affect correlations
Conclusion
This Scientific Correlation Testing Framework provides a comprehensive tool for analyzing relationships between financial assets. By offering both Pearson and Spearman correlation methods, statistical significance testing, and rolling correlation analysis, it goes beyond simple correlation measures to provide deeper insights.
For beginners, this script might seem complex, but it's built on fundamental statistical concepts that become clearer with use. Start with the default settings and focus on interpreting the main correlation lines and the statistics table. As you become more comfortable, you can adjust the parameters and explore more advanced applications.
Remember that correlation analysis is just one tool in a trader's toolkit. It should be used in conjunction with other forms of analysis and with a clear understanding of its limitations. When used properly, it can provide valuable insights for portfolio construction, risk management, and pair trading strategy development.
Statistics
LibWghtLibrary "LibWght"
This is a library of mathematical and statistical functions
designed for quantitative analysis in Pine Script. Its core
principle is the integration of a custom weighting series
(e.g., volume) into a wide array of standard technical
analysis calculations.
Key Capabilities:
1. **Universal Weighting:** All exported functions accept a `weight`
parameter. This allows standard calculations (like moving
averages, RSI, and standard deviation) to be influenced by an
external data series, such as volume or tick count.
2. **Weighted Averages and Indicators:** Includes a comprehensive
collection of weighted functions:
- **Moving Averages:** `wSma`, `wEma`, `wWma`, `wRma` (Wilder's),
`wHma` (Hull), and `wLSma` (Least Squares / Linear Regression).
- **Oscillators & Ranges:** `wRsi`, `wAtr` (Average True Range),
`wTr` (True Range), and `wR` (High-Low Range).
3. **Volatility Decomposition:** Provides functions to decompose
total variance into distinct components for market analysis.
- **Two-Way Decomposition (`wTotVar`):** Separates variance into
**between-bar** (directional) and **within-bar** (noise)
components.
- **Three-Way Decomposition (`wLRTotVar`):** Decomposes variance
relative to a linear regression into **Trend** (explained by
the LR slope), **Residual** (mean-reversion around the
LR line), and **Within-Bar** (noise) components.
- **Local Volatility (`wLRLocTotStdDev`):** Measures the total
"noise" (within-bar + residual) around the trend line.
4. **Weighted Statistics and Regression:** Provides a robust
function for Weighted Linear Regression (`wLinReg`) and a
full suite of related statistical measures:
- **Between-Bar Stats:** `wBtwVar`, `wBtwStdDev`, `wBtwStdErr`.
- **Residual Stats:** `wResVar`, `wResStdDev`, `wResStdErr`.
5. **Fallback Mechanism:** All functions are designed for reliability.
If the total weight over the lookback period is zero (e.g., in
a no-volume period), the algorithms automatically fall back to
their unweighted, uniform-weight equivalents (e.g., `wSma`
becomes a standard `ta.sma`), preventing errors and ensuring
continuous calculation.
---
**DISCLAIMER**
This library is provided "AS IS" and for informational and
educational purposes only. It does not constitute financial,
investment, or trading advice.
The author assumes no liability for any errors, inaccuracies,
or omissions in the code. Using this library to build
trading indicators or strategies is entirely at your own risk.
As a developer using this library, you are solely responsible
for the rigorous testing, validation, and performance of any
scripts you create based on these functions. The author shall
not be held liable for any financial losses incurred directly
or indirectly from the use of this library or any scripts
derived from it.
wSma(source, weight, length)
Weighted Simple Moving Average (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
the arithmetic mean if Σweight = 0.
wEma(source, weight, length)
Weighted EMA (exponential kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Exponential-kernel weighted mean; falls
back to classic EMA if Σweight = 0.
wWma(source, weight, length)
Weighted WMA (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
classic WMA if Σweight = 0.
wRma(source, weight, length)
Weighted RMA (Wilder kernel, α = 1/len).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Wilder-kernel weighted mean; falls back to
classic RMA if Σweight = 0.
wHma(source, weight, length)
Weighted HMA (linear kernel).
Parameters:
source (float) : series float Data to average.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Linear-kernel weighted mean; falls back to
classic HMA if Σweight = 0.
wRsi(source, weight, length)
Weighted Relative Strength Index.
Parameters:
source (float) : series float Price series.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Weighted RSI; uniform if Σw = 0.
wAtr(tr, weight, length)
Weighted ATR (Average True Range).
Implemented as WRMA on *true range*.
Parameters:
tr (float) : series float True Range series.
weight (float) : series float Weight series.
length (simple int) : simple int Look-back length ≥ 1.
Returns: series float Weighted ATR; uniform weights if Σw = 0.
wTr(tr, weight, length)
Weighted True Range over a window.
Parameters:
tr (float) : series float True Range series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Weighted mean of TR; uniform if Σw = 0.
wR(r, weight, length)
Weighted High-Low Range over a window.
Parameters:
r (float) : series float High-Low per bar.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 1.
Returns: series float Weighted mean of range; uniform if Σw = 0.
wBtwVar(source, weight, length, biased)
Weighted Between Variance (biased/unbiased).
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns:
variance series float The calculated between-bar variance (σ²btw), either biased or unbiased.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wBtwStdDev(source, weight, length, biased)
Weighted Between Standard Deviation.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σbtw uniform if Σw = 0.
wBtwStdErr(source, weight, length, biased)
Weighted Between Standard Error.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²btw / N_eff) uniform if Σw = 0.
wTotVar(mu, sigma, weight, length, biased)
Weighted Total Variance (= between-group + within-group).
Useful when each bar represents an aggregate with its own
mean* and pre-estimated σ (e.g., second-level ranges inside a
1-minute bar). Assumes the *weight* series applies to both the
group means and their σ estimates.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns:
varBtw series float The between-bar variance component (σ²btw).
varWtn series float The within-bar variance component (σ²wtn).
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wTotStdDev(mu, sigma, weight, length, biased)
Weighted Total Standard Deviation.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σtot.
wTotStdErr(mu, sigma, weight, length, biased)
Weighted Total Standard Error.
SE = √( total variance / N_eff ) with the same effective sample
size logic as `wster()`.
Parameters:
mu (float) : series float Group means (e.g., HL2 of 1-second bars).
sigma (float) : series float Pre-estimated σ of each group (same basis).
weight (float) : series float Weight series (volume, ticks, …).
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²tot / N_eff).
wLinReg(source, weight, length)
Weighted Linear Regression.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
Returns:
mid series float The estimated value of the regression line at the most recent bar.
slope series float The slope of the regression line.
intercept series float The intercept of the regression line.
wResVar(source, weight, midLine, slope, length, biased)
Weighted Residual Variance.
linear regression – optionally biased (population) or
unbiased (sample).
Parameters:
source (float) : series float Data series.
weight (float) : series float Weighting series (volume, etc.).
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population variance (σ²_P), denominator ≈ N_eff.
false → sample variance (σ²_S), denominator ≈ N_eff - 2.
(Adjusts for 2 degrees of freedom lost to the regression).
Returns:
variance series float The calculated residual variance (σ²res), either biased or unbiased.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wResStdDev(source, weight, midLine, slope, length, biased)
Weighted Residual Standard Deviation.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float σres; uniform if Σw = 0.
wResStdErr(source, weight, midLine, slope, length, biased)
Weighted Residual Standard Error.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
midLine (float) : series float Regression value at the last bar.
slope (float) : series float Slope per bar.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population (biased); false → sample.
Returns: series float √(σ²res / N_eff); uniform if Σw = 0.
wLRTotVar(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Variance **around the
window’s weighted mean μ**.
σ²_tot = E_w ⟶ *within-group variance*
+ Var_w ⟶ *residual variance*
+ Var_w ⟶ *trend variance*
where each bar i in the look-back window contributes
m_i = *mean* (e.g. 1-sec HL2)
σ_i = *sigma* (pre-estimated intrabar σ)
w_i = *weight* (volume, ticks, …)
ŷ_i = b₀ + b₁·x (value of the weighted LR line)
r_i = m_i − ŷ_i (orthogonal residual)
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns:
varRes series float The residual variance component (σ²res).
varWtn series float The within-bar variance component (σ²wtn).
varTrd series float The trend variance component (σ²trd), explained by the linear regression.
sumW series float The sum of weights over the lookback period (Σw).
sumW2 series float The sum of squared weights over the lookback period (Σw²).
wLRTotStdDev(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Standard Deviation.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √(σ²tot).
wLRTotStdErr(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Total Standard Error.
SE = √( σ²_tot / N_eff ) with N_eff = Σw² / Σw² (like in wster()).
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √((σ²res, σ²wtn, σ²trd) / N_eff).
wLRLocTotStdDev(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Local Total Standard Deviation.
Measures the total "noise" (within-bar + residual) around the trend.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √(σ²wtn + σ²res).
wLRLocTotStdErr(mu, sigma, weight, midLine, slope, length, biased)
Weighted Linear-Regression Local Total Standard Error.
Parameters:
mu (float) : series float Per-bar mean m_i.
sigma (float) : series float Pre-estimated σ_i of each bar.
weight (float) : series float Weight series w_i (≥ 0).
midLine (float) : series float Regression value at the latest bar (ŷₙ₋₁).
slope (float) : series float Slope b₁ of the regression line.
length (int) : series int Look-back length ≥ 2.
biased (bool) : series bool true → population; false → sample.
Returns: series float √((σ²wtn + σ²res) / N_eff).
wLSma(source, weight, length)
Weighted Least Square Moving Average.
Parameters:
source (float) : series float Data series.
weight (float) : series float Weight series.
length (int) : series int Look-back length ≥ 2.
Returns: series float Least square weighted mean. Falls back
to unweighted regression if Σw = 0.
Central Limit Theorem Reversion IndicatorDear TV community, let me introduce you to the first-ever Central Limit Theorem indicator on TradingView.
The Central Limit Theorem is used in statistics and it can be quite useful in quant trading and understanding market behaviors.
In short, the CLT states: "When you take repeated samples from any population and calculate their averages, those averages will form a normal (bell curve) distribution—no matter what the original data looks like."
In this CLT indicator, I use statistical theory to identify high-probability mean reversion opportunities in the markets. It calculates statistical confidence bands and z-scores to identify when price movements deviate significantly from their expected distribution, signaling potential reversion opportunities with quantifiable probability levels.
Mathematical Foundation
The Central Limit Theorem (CLT) says that when you average many data points together, those averages will form a predictable bell-curve pattern, even if the original data is completely random and unpredictable (which often is in the markets). This works no matter what you're measuring, and it gets more reliable as you use more data points.
Why using it for trading?
Individual price movements seem random and chaotic, but when we look at the average of many price movements, we can actually predict how they should behave statistically. This lets us spot when prices have moved "too far" from what's normal—and those extreme moves tend to snap back (mean reversion).
Key Formula:
Z = (X̄ - μ) / (σ / √n)
Where:
- X̄ = Sample mean (average return over n periods)
- μ = Population mean (long-term expected return)
- σ = Population standard deviation (volatility)
- n = Sample size
- σ/√n = Standard error of the mean
How I Apply CLT
Step 1: Calculate Returns
Measures how much price changed from one bar to the next (using logarithms for better statistical properties)
Step 2: Average Recent Returns
Takes the average of the last n returns (e.g., last 100 bars). This is your "sample mean."
Step 3: Find What's "Normal"
Looks at historical data to determine: a) What the typical average return should be (the long-term mean) and b) How volatile the market usually is (standard deviation)
Step 4: Calculate Standard Error
Determines how much sample averages naturally vary. Larger samples = smaller expected variation.
Step 5: Calculate Z-Score
Measures how unusual the current situation is.
Step 6: Draw Confidence Bands
Converts these statistical boundaries into actual price levels on your chart, showing where price is statistically expected to stay 95% and 99% of the time.
Interpretation & Usage
The Z-Score:
The z-score tells you how statistically unusual the current price deviation is:
|Z| < 1.0 → Normal behavior, no action
|Z| = 1.0 to 1.96 → Moderate deviation, watch closely
|Z| = 1.96 to 2.58 → Significant deviation (95%+), consider entry
|Z| > 2.58 → Extreme deviation (99%+), high probability setup
The Confidence Bands
- Upper Red Bands: 95% and 99% overbought zones → Expect mean reversion downward as the price is not likely to cross these lines.
- Center Gray Line: Statistical expectation (fair value)
- Lower Blue Bands: 95% and 99% oversold zones → Expect mean reversion upward
Trading Logic:
- When price exceeds the upper 95% band (z-score > +1.96), there's only a 5% probability this is random noise → Strong sell/short signal
- When price falls below the lower 95% band (z-score < -1.96), there's a 95% statistical expectation of upward reversion → Strong buy/long signal
Background Gradient
The background color provides real-time visual feedback:
- Blue shades: Oversold conditions, expect upward reversion
- Red shades: Overbought conditions, expect downward reversion
- Intensity: Darker colors indicate stronger statistical significance
Trading Strategy Examples
Hypothetically, this is how the indicator could be used:
- Long: Z-score < -1.96 (below 95% confidence band)
- Short: Z-score > +1.96 (above 95% confidence band)
- Take profit when price returns to center line (Z ≈ 0)
Input Parameters
Sample Size (n) - Default: 100
Lookback Period (m) - Default: 100
You can also create alerts based on the indicator.
Final notes:
- The indicator uses logarithmic returns for better statistical properties
- Converts statistical bands back to price space for practical use
- Adaptive volatility: Bands automatically widen in high volatility, narrow in low volatility
- No repainting: yay! All calculations use historical data only
Feedback is more than welcome!
Henri
Stablecoin Liquidity Delta (Aggregate Market Cap Flow)Hi All,
This indicator visualizes the bar-to-bar change in the aggregate market capitalization of major stablecoins, including USDT, USDC, DAI, and others. It serves as a proxy for monitoring on-chain liquidity and measuring capital inflows or outflows across the crypto market.
Stablecoins are the primary liquidity layer of the crypto economy. Their combined market capitalization acts as a mirror of the available fiat-denominated liquidity in digital markets:
🟩 An increase in the total stablecoin market capitalization indicates new issuance (capital entering the market).
🟥 A decrease reflects redemption or burning (liquidity exiting the system).
Tracking these flows helps anticipate macro-level liquidity trends that often lead overall market direction, providing context for broader price movements.
All values are derived from TradingView’s public CRYPTOCAP tickers, which represent the market capitalization of each stablecoin. While minor deviations can occur due to small price fluctuations around the $1 peg, these figures serve as a proxy for circulating supply and net issuance across the stablecoin ecosystem.
Continuation Probability (0–100)This indicator helps measure how likely the current candle trend will continue or reverse, giving a probability score between 0–100.
It combines multiple market factors trend, candle strength, volume, and volatility to create a single, intuitive signal.
Simple FloatFloat Display Indicator
A simple, clean indicator that displays the current float (shares outstanding float) for any stock directly in your indicator status line at the top left of the chart.
Features:
- Shows the float value with automatic K/M formatting for thousands and millions
- No chart clutter - value only appears in the status line, nothing plotted on the chart
- Works on any stock that has float data available
- Lightweight and efficient
Perfect for traders who want quick access to float information without switching between windows or cluttering their charts.
Note: Float data availability depends on TradingView's financial data for the specific ticker. Some tickers may not have this data available.
Vandan V2Vandan V2 is an automated trend-following strategy for NASDAQ E-mini Futures (NQ1!).
It uses multi-timeframe momentum and volatility filters to identify high-probability entries.
Includes dynamic risk management and trailing logic optimized for intraday trading.
Risk Position Sizer (Entry=Close, Stop=Daily Low)This is for trading stocks/shares. Its main goal is to help you gauge how big or how small of a position you should add based on your account size.
Info Box⚙️ Purpose
Shows useful trade and event-related data such as:
% Distance from stop levels (D, DH)
Earnings countdown in bars
All displayed in a single floating info box (table) on the chart.
📋 Key Features
Customizable Display
Choose table position (Top Right, Bottom Center, etc.)
Choose table size (Auto, Large, Tiny, etc.)
Custom text and background colors
Metrics Shown
D: % Distance from stop (difference between close and low/high)
DH: % Distance from midpoint of the candle
Earnings Countdown: Number of bars until next earnings event
Conditional Styling
If earnings are within 3 bars, text color turns red as a warning.
Execution Conditions
Runs only on daily timeframe
Updates on last bar only (no historical clutter)
Output
Displays all selected metrics in one line, separated by “×”
e.g. → D: -2.1% × 5 × DH: 1.4%
🧩 Overall Function
Creates a clean, customizable “info box” showing trade distances and upcoming earnings countdown for quick decision-making directly on your TradingView chart.
Nqaba Goldminer StrategyThis indicator plots the New York session key timing levels used in institutional intraday models.
It automatically marks the 03:00 AM, 10:00 AM, and 2:00 PM (14:00) New York times each day:
Vertical lines show exactly when those time windows open — allowing traders to identify major global liquidity shifts between London, New York, and U.S. session overlaps.
Horizontal lines mark the opening price of the 5-minute candle that begins at each of those key times, providing precision reference levels for potential reversals, continuation setups, and intraday bias shifts.
Users can customize each line’s color, style (solid/dashed/dotted), width, and horizontal-line length.
A history toggle lets you display all past occurrences or just today’s key levels for a cleaner chart.
These reference levels form the foundation for strategies such as:
London Breakout to New York Reversal models
Opening Range / Session Open bias confirmation
Institutional volume transfer windows (London → NY → Asia)
The tool provides a simple visual structure for traders to frame intraday decision-making around recurring institutional time events.
Percentile Rank Oscillator (Price + VWMA)A statistical oscillator designed to identify potential market turning points using percentile-based price analytics and volume-weighted confirmation.
What is PRO?
Percentile Rank Oscillator measures how extreme current price behavior is relative to its own recent history. It calculates a rolling percentile rank of price midpoints and VWMA deviation (volume-weighted price drift). When price reaches historically rare levels – high or low percentiles – it may signal exhaustion and potential reversal conditions.
How it works
Takes midpoint of each candle ((H+L)/2)
Ranks the current value vs previous N bars using rolling percentile rank
Maps percentile to a normalized oscillator scale (-1..+1 or 0–100)
Optionally evaluates VWMA deviation percentile for volume-confirmed signals
Highlights extreme conditions and confluence zones
Why percentile rank?
Median-based percentiles ignore outliers and read the market statistically – not by fixed thresholds. Instead of guessing “overbought/oversold” values, the indicator adapts to current volatility and structure.
Key features
Rolling percentile rank of price action
Optional VWMA-based percentile confirmation
Adaptive, noise-robust structure
User-selectable thresholds (default 95/5)
Confluence highlighting for price + VWMA extremes
Optional smoothing (RMA)
Visual extreme zone fills for rapid signal recognition
How to use
High percentile values –> statistically extreme upward deviation (potential top)
Low percentile values –> statistically extreme downward deviation (potential bottom)
Price + VWMA confluence strengthens reversal context
Best used as part of a broader trading framework (market structure, order flow, etc.)
Tip: Look for percentile spikes at key HTF levels, after extended moves, or where liquidity sweeps occur. Strong moves into rare percentile territory may precede mean reversion.
Suggested settings
Default length: 100 bars
Thresholds: 95 / 5
Smoothing: 1–3 (optional)
Important note
This tool does not predict direction or guarantee outcomes. It provides statistical context for price extremes to help traders frame probability and timing. Always combine with sound risk management and other tools.
Multi-Mode Seasonality Map [BackQuant]Multi-Mode Seasonality Map
A fast, visual way to expose repeatable calendar patterns in returns, volatility, volume, and range across multiple granularities (Day of Week, Day of Month, Hour of Day, Week of Month). Built for idea generation, regime context, and execution timing.
What is “seasonality” in markets?
Seasonality refers to statistically repeatable patterns tied to the calendar or clock, rather than to price levels. Examples include specific weekdays tending to be stronger, certain hours showing higher realized volatility, or month-end flow boosting volumes. This tool measures those effects directly on your charted symbol.
Why seasonality matters
It’s orthogonal alpha: timing edges independent of price structure that can complement trend, mean reversion, or flow-based setups.
It frames expectations: when a session typically runs hot or cold, you size and pace risk accordingly.
It improves execution: entering during historically favorable windows, avoiding historically noisy windows.
It clarifies context: separating normal “calendar noise” from true anomaly helps avoid overreacting to routine moves.
How traders use seasonality in practice
Timing entries/exits : If Tuesday morning is historically weak for this asset, a mean-reversion buyer may wait for that drift to complete before entering.
Sizing & stops : If 13:00–15:00 shows elevated volatility, widen stops or reduce size to maintain constant risk.
Session playbooks : Build repeatable routines around the hours/days that consistently drive PnL.
Portfolio rotation : Compare seasonal edges across assets to schedule focus and deploy attention where the calendar favors you.
Why Day-of-Week (DOW) can be especially helpful
Flows cluster by weekday (ETF creations/redemptions, options hedging cadence, futures roll patterns, macro data releases), so DOW often encodes a stable micro-structure signal.
Desk behavior and liquidity provision differ by weekday, impacting realized range and slippage.
DOW is simple to operationalize: easy rules like “fade Monday afternoon chop” or “press Thursday trend extension” can be tested and enforced.
What this indicator does
Multi-mode heatmaps : Switch between Day of Week, Day of Month, Hour of Day, Week of Month .
Metric selection : Analyze Returns , Volatility ((high-low)/open), Volume (vs 20-bar average), or Range (vs 20-bar average).
Confidence intervals : Per cell, compute mean, standard deviation, and a z-based CI at your chosen confidence level.
Sample guards : Enforce a minimum sample size so thin data doesn’t mislead.
Readable map : Color palettes, value labels, sample size, and an optional legend for fast interpretation.
Scoreboard : Optional table highlights best/worst DOW and today’s seasonality with CI and a simple “edge” tag.
How it’s calculated (under the hood)
Per bar, compute the chosen metric (return, vol, volume %, or range %) over your lookback window.
Bucket that metric into the active calendar bin (e.g., Tuesday, the 15th, 10:00 hour, or Week-2 of month).
For each bin, accumulate sum , sum of squares , and count , then at render compute mean , std dev , and confidence interval .
Color scale normalizes to the observed min/max of eligible bins (those meeting the minimum sample size).
How to read the heatmap
Color : Greener/warmer typically implies higher mean value for the chosen metric; cooler implies lower.
Value label : The center number is the bin’s mean (e.g., average % return for Tuesdays).
Confidence bracket : Optional “ ” shows the CI for the mean, helping you gauge stability.
n = sample size : More samples = more reliability. Treat small-n bins with skepticism.
Suggested workflows
Pick the lens : Start with Analysis Type = Returns , Heatmap View = Day of Week , lookback ≈ 252 trading days . Note the best/worst weekdays and their CI width.
Sanity-check volatility : Switch to Volatility to see which bins carry the most realized range. Use that to plan stop width and trade pacing.
Check liquidity proxy : Flip to Volume , identify thin vs thick windows. Execute risk in thicker windows to reduce slippage.
Drill to intraday : Use Hour of Day to reveal opening bursts, lunchtime lulls, and closing ramps. Combine with your main strategy to schedule entries.
Calendar nuance : Inspect Week of Month and Day of Month for end-of-month, options-cycle, or data-release effects.
Codify rules : Translate stable edges into rules like “no fresh risk during bottom-quartile hours” or “scale entries during top-quartile hours.”
Parameter guidance
Analysis Period (Days) : 252 for a one-year view. Shorten (100–150) to emphasize the current regime; lengthen (500+) for long-memory effects.
Heatmap View : Start with DOW for robustness, then refine with Hour-of-Day for your execution window.
Confidence Level : 95% is standard; use 90% if you want wider coverage with fewer false “insufficient data” bins.
Min Sample Size : 10–20 helps filter noise. For Hour-of-Day on higher timeframes, consider lowering if your dataset is small.
Color Scheme : Choose a palette with good mid-tone contrast (e.g., Red-Green or Viridis) for quick thresholding.
Interpreting common patterns
Return-positive but low-vol bins : Favorable drift windows for passive adds or tight-stop trend continuation.
Return-flat but high-vol bins : Opportunity for mean reversion or breakout scalping, but manage risk accordingly.
High-volume bins : Better expected execution quality; schedule size here if slippage matters.
Wide CI : Edge is unstable or sample is thin; treat as exploratory until more data accumulates.
Best practices
Revalidate after regime shifts (new macro cycle, liquidity regime change, major exchange microstructure updates).
Use multiple lenses: DOW to find the day, then Hour-of-Day to refine the entry window.
Combine with your core setup signals; treat seasonality as a filter or weight, not a standalone trigger.
Test across assets/timeframes—edges are instrument-specific and may not transfer 1:1.
Limitations & notes
History-dependent: short histories or sparse intraday data reduce reliability.
Not causal: a hot Tuesday doesn’t guarantee future Tuesday strength; treat as probabilistic bias.
Aggregation bias: changing session hours or symbol migrations can distort older samples.
CI is z-approximate: good for fast triage, not a substitute for full hypothesis testing.
Quick setup
Use Returns + Day of Week + 252d to get a clean yearly map of weekday edge.
Flip to Hour of Day on intraday charts to schedule precise entries/exits.
Keep Show Values and Confidence Intervals on while you calibrate; hide later for a clean visual.
The Multi-Mode Seasonality Map helps you convert the calendar from an afterthought into a quantitative edge, surfacing when an asset tends to move, expand, or stay quiet—so you can plan, size, and execute with intent.
Market SessionsMarket Sessions (Asian, London, NY, Pacific)
Summary
This indicator plots the main global market sessions (Asian, European, American, Pacific) as boxes on your chart, complete with dynamic high/low tracking.
It's an essential tool for intraday traders to track session-based volatility patterns and visualize key support/resistance levels (like the Asian Range) that often define price action for the rest of the day.
Who it’s for
Intraday traders, scalpers, and day traders who need to visualize market hours and session-based ranges. If your strategy depends on the London open, the New York close, or the Asian range, this script will map it out for you.
What it shows
Customizable Session Boxes: Four fully configurable boxes for the Asian, European (London), American (New York), and Pacific (Sydney) sessions.
Session High & Low: The script tracks and boxes the highest high and lowest low of each session, dynamically updating as the session progresses.
Session Labels: Clear labels (e.g., "AS", "EU") mark each session, anchored to the start time.
Key Features
Powerful Timezone Control: This is the core feature.
Use Exchange Timezone (Default): Simply enter session times (e.g., 8:00 for London) relative to the exchange's timezone (e.g., "NASDAQ" or "BINANCE").
Use UTC Offset: Uncheck the box and enter a UTC offset (e.g., +3 or -5). Now, all session times you enter are relative to that specific UTC offset. This gives you full control regardless of the chart you're on.
Fully Customizable: Toggle any session on/off.
Style Control: Change the fill color, border color, transparency, border width, and line style (Solid, Dashed, Dotted) for each session individually.
Smart Labels: Labels stay anchored to the start of the session (no "sliding") and float just above the session high.
Why this helps
Track Volatility & Market Behavior: Visually identify the "personality" of each session. Some sessions might consistently produce powerful pumps or dumps, while others are prone to sideways "chop" or accumulation. This indicator helps you see these repeating patterns.
Find Key Support/Resistance Levels: The High and Low of a session (e.g., the Asian Range) often become critical support and resistance levels for the next session (e.g., London). This script makes it easy to spot these "session-to-session" S/R flips and reactions.
Aid Statistical Analysis: The script provides the core visual data for your statistical research. You can easily track how often the London session breaks the Asian high, or which session is most likely to reverse the trend, helping you build a robust trading plan.
Context is King: Instantly see which market is active, which are overlapping (like the high-volume London-NY overlap), and which have closed.
Quick setup
Go to Timezone Settings.
Decide how you want to enter times:
Easy (Default): Leave Use Exchange Timezone checked. Enter session times based on the chart's native exchange (e.g., for BTC/USDT on Binance, use UTC+0 times).
Manual (Pro): Uncheck Use Exchange Timezone. Enter your UTC Offset (e.g., +2 for Berlin). Now, enter all session times as they appear on the clock in Berlin.
Go to each session tab (Asian, European...) to enable/disable it and set the correct start/end hours and minutes.
Style the colors to match your chart theme.
Disclaimer
For educational/informational purposes only; not financial advice. Trading involves risk—manage it responsibly.
NFCI National Financial Conditions IndexChicago Fed National Financial Conditions Index (NFCI)
This indicator plots the Chicago Fed’s National Financial Conditions Index (NFCI).
The NFCI updates weekly, and its latest value is displayed across all chart intervals.
The NFCI measures how tight or loose overall U.S. financial conditions are. It combines over 100 weekly indicators from the money, bond, and equity markets—along with credit and leverage data—into a single composite index.
The NFCI has three key subcomponents, each of which can be independently selected within the indicator:
Risk: Captures volatility, credit spreads, and overall market stress.
Credit: Tracks how easy or difficult it is to borrow across households and businesses.
Leverage: Reflects the level of debt and balance-sheet strength in the financial system.
When the NFCI rises, financial conditions are tightening — liquidity is contracting, borrowing costs are climbing, and investors tend to reduce risk.
When the NFCI falls, conditions are loosening — liquidity expands, credit flows more freely, and markets generally become more risk-seeking.
Traders often use the NFCI as a macro backdrop for risk appetite: rising values signal growing stress and defensive positioning, while falling values indicate improving liquidity and a more supportive market environment.
Rolling Correlation vs Another Symbol (SPY Default)This indicator visualizes the rolling correlation between the current chart symbol and another selected asset, helping traders understand how closely the two move together over time.
It calculates the Pearson correlation coefficient over a user-defined period (default 22 bars) and plots it as a color-coded line:
• Green line → positive correlation (move in the same direction)
• Red line → negative correlation (move in opposite directions)
• A gray dashed line marks the zero level (no correlation).
The background highlights periods of strong relationship:
• Light green when correlation > +0.7 (strong positive)
• Light red when correlation < –0.7 (strong negative)
Use this tool to quickly spot diversification opportunities, confirm hedges, or understand how assets interact during different market regimes.
Standardization (Z-score)Standardization, often referred to as Z-score normalization, is a data preprocessing technique that rescales data to have a mean of 0 and a standard deviation of 1. The resulting values, known as Z-scores, indicate how many standard deviations an individual data point is from the mean of the dataset (or a rolling sample of it).
This indicator calculates and plots the Z-score for a given input series over a specified lookback period. It is a fundamental tool for statistical analysis, outlier detection, and preparing data for certain machine learning algorithms.
## Core Concepts
* **Standardization:** The process of transforming data to fit a standard normal distribution (or more generally, to have a mean of 0 and standard deviation of 1).
* **Z-score (Standard Score):** A dimensionless quantity that represents the number of standard deviations by which a data point deviates from the mean of its sample.
The formula for a Z-score is:
`Z = (x - μ) / σ`
Where:
* `x` is the individual data point (e.g., current value of the source series).
* `μ` (mu) is the mean of the sample (calculated over the lookback period).
* `σ` (sigma) is the standard deviation of the sample (calculated over the lookback period).
* **Mean (μ):** The average value of the data points in the sample.
* **Standard Deviation (σ):** A measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
## Common Settings and Parameters
| Parameter | Type | Default | Function | When to Adjust |
| :-------------- | :----------- | :------ | :------------------------------------------------------------------------------------------------------ | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Source | series float | close | The input data series (e.g., price, volume, indicator values). | Choose the series you want to standardize. |
| Lookback Period | int | 20 | The number of bars (sample size) used for calculating the mean (μ) and standard deviation (σ). Min 2. | A larger period provides more stable estimates of μ and σ but will be less responsive to recent changes. A shorter period is more reactive. `minval` is 2 because `ta.stdev` requires it. |
**Pro Tip:** Z-scores are excellent for identifying anomalies or extreme values. For instance, applying Standardization to trading volume can help quickly spot days with unusually high or low activity relative to the recent norm (e.g., Z-score > 2 or < -2).
## Calculation and Mathematical Foundation
The Z-score is calculated for each bar as follows, using a rolling window defined by the `Lookback Period`:
1. **Calculate Mean (μ):** The simple moving average (`ta.sma`) of the `Source` data over the specified `Lookback Period` is calculated. This serves as the sample mean `μ`.
`μ = ta.sma(Source, Lookback Period)`
2. **Calculate Standard Deviation (σ):** The standard deviation (`ta.stdev`) of the `Source` data over the same `Lookback Period` is calculated. This serves as the sample standard deviation `σ`.
`σ = ta.stdev(Source, Lookback Period)`
3. **Calculate Z-score:**
* If `σ > 0`: The Z-score is calculated using the formula:
`Z = (Current Source Value - μ) / σ`
* If `σ = 0`: This implies all values in the lookback window are identical (and equal to the mean). In this case, the Z-score is defined as 0, as the current source value is also equal to the mean.
* If `σ` is `na` (e.g., insufficient data in the lookback period), the Z-score is `na`.
> 🔍 **Technical Note:**
> * The `Lookback Period` must be at least 2 for `ta.stdev` to compute a valid standard deviation.
> * The Z-score calculation uses the sample mean and sample standard deviation from the rolling lookback window.
## Interpreting the Z-score
* **Magnitude and Sign:**
* A Z-score of **0** means the data point is identical to the sample mean.
* A **positive Z-score** indicates the data point is above the sample mean. For example, Z = 1 means the point is 1 standard deviation above the mean.
* A **negative Z-score** indicates the data point is below the sample mean. For example, Z = -1 means the point is 1 standard deviation below the mean.
* **Typical Range:** For data that is approximately normally distributed (bell-shaped curve):
* About 68% of Z-scores fall between -1 and +1.
* About 95% of Z-scores fall between -2 and +2.
* About 99.7% of Z-scores fall between -3 and +3.
* **Outlier Detection:** Z-scores significantly outside the -2 to +2 range, and especially outside -3 to +3, are often considered outliers or extreme values relative to the recent historical data in the lookback window.
* **Volatility Indication:** When applied to price, large absolute Z-scores can indicate moments of high volatility or significant deviation from the recent price trend.
The indicator plots horizontal lines at ±1, ±2, and ±3 standard deviations to help visualize these common thresholds.
## Common Applications
1. **Outlier Detection:** Identifying data points that are unusual or extreme compared to the rest of the sample. This is a primary use in financial markets for spotting abnormal price moves, volume spikes, etc.
2. **Comparative Analysis:** Allows for comparison of scores from different distributions that might have different means and standard deviations. For example, comparing the Z-score of returns for two different assets.
3. **Feature Scaling in Machine Learning:** Standardizing features to have a mean of 0 and standard deviation of 1 is a common preprocessing step for many machine learning algorithms (e.g., SVMs, logistic regression, neural networks) to improve performance and convergence.
4. **Creating Normalized Oscillators:** The Z-score itself can be used as a bounded (though not strictly between -1 and +1) oscillator, indicating how far the current price has deviated from its moving average in terms of standard deviations.
5. **Statistical Process Control:** Used in quality control charts to monitor if a process is within expected statistical limits.
## Limitations and Considerations
* **Assumption of Normality for Probabilistic Interpretation:** While Z-scores can always be calculated, the probabilistic interpretations (e.g., "68% of data within ±1σ") strictly apply to normally distributed data. Financial data is often not perfectly normal (e.g., it can have fat tails).
* **Sensitivity of Mean and Standard Deviation to Outliers:** The sample mean (μ) and standard deviation (σ) used in the Z-score calculation can themselves be influenced by extreme outliers within the lookback period. This can sometimes mask or exaggerate the Z-score of other points.
* **Choice of Lookback Period:** The Z-score is highly dependent on the `Lookback Period`. A short period makes it very sensitive to recent fluctuations, while a long period makes it smoother and less responsive. The appropriate period depends on the analytical goal.
* **Stationarity:** For time series data, Z-scores are calculated based on a rolling window. This implicitly assumes some level of local stationarity (i.e., the mean and standard deviation are relatively stable within the window).
Multi-Session Viewer and AnalyzerFully customizable multi-session viewer that takes session analysis to the next level. It allows you to fully customize each session to your liking. Includes a feature that highlights certain periods of time on the chart and a Time Range Marker.
It helps you analyze the instrument that you trade and pinpoint which times are more volatile than others. It also helps you choose the best time to trade your instrument and align your life schedule with the market.
NZDUSD Example:
- 3 major sessions displayed.
- Although this is NZDUSD, Sydney is not the best time to trade this pair. Volatility picks up at Tokyo open.
- I have time to trade in the evening from 18:00 to 22:00 PST. I live in a different time zone, whereas market is based on EST. How does the pair behave during the time I am available to trade based on my time zone? Time Range Marker feature allows you to see this clearly on the chart (black lines).
- I have some time in the morning to trade during New York session, but there is no way I am waking up at 05:00 PST. 06:30 PST seems doable. Blue highlighted area is good time to trade during New York session based on what Bob said. It seem like this aligns with when I am available and when I am able to trade. Volatility is also at its peak.
- I am also available to trade between London close and Tokyo open on some days of the week, but... based on what I see, green highlighted area is clearly showing that I probably don't want to waste my time trading this pair from London close and until Tokyo open. I will use this time for something else rather than be stuck in a range.
Forex Dynamic Lot Size CalculatorForex Dynamic Lot Size Calculator for Forex. Works on USD Base and USD Quote pairs. Provides real-time data based on stop-loss location. Allows you to know in real-time how the number of lots you need to purchase to match your risk %.
Number of Lots is calculated based on total risk. Total risk is calculated based on Stop-Loss + Commission + Spread Fees + Slippage measured in pips. Also includes data such as break-even pips, net take profit, margin required, buying power used, and a few others. All are real-time and anchored to the current price.
The intention of creating this indicator is to help with risk management. You know exactly how many lots you need to get this very moment to have your total risk at lets say $250, which includes commission fees, spread fees, and slippage.
To put it simply, if I was to enter the trade right now and willing to risk exactly $250, how many lots will I need to get right this second?
---
- To use adjust Account Settings along with other variables.
- Stop Loss Mode can be Manual or Dynamic. If you select Dynamic, then you will have to adjust Stop Loss Level to where you can see the reference line on the screen. It is at 1.1 by default. Just enter current price and the line will appear. Adjust it by dragging it to where you want your stop loss to be.
- Take Profit Mode can also be Manual or Dynamic. I just keep my TP at Manual and use Quick Access to set Quick RR levels.
- Adjust Spreads and Slippage to your liking. I tried to have TV calculate current spread, but it seem like it doesn't have access to real-life data for me like MT5 does. I just use average instead. Both are optional, depending on your broker and type of account you use.
- Pip Value for the current pair, Return on Margin, and Break-even line can be turned on and off, based on your needs. I just get the Break-even value in pips from the pannel and use that as reference where I need to relocate my stop loss to break-ever (commission + spreds + slippage).
- Panel is fully customizable based on your liking. Important fields are highlighted along with reference lines.
Risk Leverage ToolRisk Leverage Tool – Calculate Position Size and Required Leverage
This script automatically calculates the optimal position size and the leverage needed based on the amount of capital you are willing to risk on a trade. It is designed for traders who want precise control over their risk management.
The script determines the distance between the entry and stop-loss price, calculates the maximum position size that fits within the defined risk, and derives the notional value of the trade. Based on the available margin, it then calculates the required leverage. It also displays the percentage of margin at risk if the stop-loss is hit.
All results are displayed in a table in the top-right corner of the chart. Additionally, a label appears at the entry price level showing the same data.
To use the tool, simply input your planned entry price, stop-loss price, the maximum risk amount in dollars, and the available margin in the settings menu. The script will update all values automatically in real time.
This tool works with any market where capital risk is expressed in absolute terms (such as USD), including futures, CFDs, and leveraged spot positions. For inverse contracts or percentage-based stops, manual adjustment is required.
Adaptive Trend SelectorThe Adaptive Trend Selector is a comprehensive trend-following tool designed to automatically identify the optimal moving average crossover strategy. It features adjustable parameters and an integrated backtester that delivers institutional-grade insights into the recommended strategy. The model continuously adapts to new data in real time by evaluating multiple moving average combinations, determining the best performing lengths, and presenting the backtest results in a clear, color-coded table that benchmarks performance against the buy-and-hold strategy.
At its core, the model systematically backtests a wide range of moving average combinations to identify the configuration that maximizes the selected optimization metric. Users can choose to optimize for absolute returns or risk-adjusted returns using the Sharpe, Sortino, or Calmar ratios. Alternatively, users can enable manual optimization to test custom fast and slow moving average lengths and view the corresponding backtest results. The label displays the Compounded Annual Growth Rate (CAGR) of the strategy, with the buy-and-hold CAGR in parentheses for comparison. The table presents the backtest results based on the fast and slow lengths displayed at the top:
Sharpe = CAGR per unit of standard deviation.
Sortino = CAGR per unit of downside deviation.
Calmar = CAGR relative to maximum drawdown.
Max DD = Largest peak-to-trough decline in value.
Beta (β) = Return sensitivity relative to buy-and-hold.
Alpha (α) = Excess annualized risk-adjusted returns.
Win Rate = Ratio of profitable trades to total trades.
Profit Factor = Total gross profit per unit of losses.
Expectancy = Average expected return per trade.
Trades/Year = Average number of trades per year.
This indicator is designed with flexibility in mind, enabling users to specify the start date of the backtesting period and the preferred moving average strategy. Supported strategies include the Exponential Moving Average (EMA), Simple Moving Average (SMA), Wilder’s Moving Average (RMA), Weighted Moving Average (WMA), and Volume-Weighted Moving Average (VWMA). To minimize overfitting, users can define constraints such as a minimum and maximum number of trades per year, as well as an optional optimization margin that prioritizes longer, more robust combinations by requiring shorter-length strategies to exceed this threshold. The table follows an intuitive color logic that enables quick performance comparison against buy-and-hold (B&H):
Sharpe = Green indicates better than B&H, while red indicates worse.
Sortino = Green indicates better than B&H, while red indicates worse.
Calmar = Green indicates better than B&H, while red indicates worse.
Max DD = Green indicates better than B&H, while red indicates worse.
Beta (β) = Green indicates better than B&H, while red indicates worse.
Alpha (α) = Green indicates above 0%, while red indicates below 0%.
Win Rate = Green indicates above 50%, while red indicates below 50%.
Profit Factor = Green indicates above 2, while red indicates below 1.
Expectancy = Green indicates above 0%, while red indicates below 0%.
In summary, the Adaptive Trend Selector is a powerful tool designed to help investors make data-driven decisions when selecting moving average crossover strategies. By optimizing for risk-adjusted returns, investors can confidently identify the best lengths using institutional-grade metrics. While results are based on the selected historical period, users should be mindful of potential overfitting, as past results may not persist under future market conditions. Since the model recalibrates to incorporate new data, the recommended lengths may evolve over time.
Mercury Retrograde — Daily boxes & bottom % (stable v6)水星逆行のアノマリー検証。対象は日経225の過去5年の値動き。水星逆行開始時の終値と水星逆行終了時の終値を比較。上昇率・下落率に応じて色分け。
Verification of Mercury Retrograde Anomalies. Subject: Nikkei 225 price movements over the past five years. Comparing closing prices at the start and end of Mercury retrograde periods. Color-coded based on percentage increase/decrease.
Lump Sum Favorability (SPX & NDX)This indicator provides a visual dashboard to gauge the statistical favorability of deploying a "Lump Sum" investment into the SPX (S&P 500) or NDX (Nasdaq 100).
The primary goal is not to time the exact market bottom, but to identify zones of significant pessimism or euphoria. Historically, periods of indiscriminate selling have represented high-probability entry points for long-term investors.
The dashboard consists of two parts:
1. The Favorability Gauge: A 12-segment gauge that moves from Red (Unfavorable) to Teal (Favorable).
2. The Summary Text: An optional text box (enabled in settings) that provides a plain-English summary of the current market breadth.
---
The Method: Market Breadth
This indicator is not based on the price of the index itself. Price-based indicators (like an RSI on the SPX) can be misleading. In a market-cap-weighted index, a few mega-cap stocks can hold the index price up while the vast majority of "average" stocks are already in a deep bear market.
This tool uses Market Breadth to measure the true, underlying health and participation of the entire market.
How It Works
1. Data Source: The indicator pulls the daily percentage of companies within the selected index (SPX or NDX) that are trading above their 200-day moving average. (Data tickers: S5TH for SPX, NDTH for NDX).
2. Smoothing: This raw data is volatile. To filter out daily noise and confirm a persistent trend, the indicator calculates a 5-day Simple Moving Average (SMA) of this percentage. This is the value used by the indicator.
3. Interpretation:
High Value (>= 50%): More than half of the stocks are above their long-term average. This signifies the market is "Overheated" or in a risk-on phase. The favorability for a new lump sum investment is considered Low.
Low Value (< 50%): Less than half of the stocks are above their long-term average. This signifies "Oversold" conditions or capitulation. These moments historically offer the best favorability for starting a new long-term investment.
---
How to Use the Indicator
1. The Favorability Gauge
The gauge is designed to be intuitive: Red means "Stop/Caution," and Teal means "Go/Opportunity."
Note: The gauge's logic is inverted from the data value to achieve this simplicity.
Red Zone (Left): UNFAVORABLE
This corresponds to a high percentage of stocks being above their 200d MA (>= 50%). The market is considered Overheated, and the favorability for a new lump sum investment is low.
Teal Zone (Right): FAVORABLE
This corresponds to a low percentage of stocks being above their 200d MA (< 50%). The market is considered Oversold, and the favorability for a new lump sum investment is high.
2. The Summary Text
When "Show Summary Text" is enabled in the settings, a box will appear at the top-center of your chart. This box provides a clear, data-driven summary, such as:
"Currently, only 22% of S&P 500 companies are above their 200-day MA. Market is Oversold."
The color of this text will automatically change to match the market state (Red for Overheated, Teal for Oversold), providing instant confirmation of the gauge's reading.
---
Settings
Market: Choose the index to analyze: SPX (S&P 500) or NDX (Nasdaq 100).
Gauge Position: Select where the gauge dashboard should appear on your chart (default is Bottom Right).
Show Summary Text: Toggle the descriptive text box on or off (default is On).
---
This indicator is a statistical and historical guide, not a financial advice or timing signal. It is designed to measure favorability based on past market behavior, not to provide certainty.
Extreme oversold conditions can persist, and markets can always go lower. This tool should be used as one component of a broader investment and risk-management framework. Past performance is not a guarantee of future results.
GARCH Range PredictorThis was inspired by deltatrendtrading's video on GARCH models to predict daily trading ranges and identify favorable trading conditions. Based on advanced volatility forecasting techniques, it predicts whether a trading day's true range will exceed a threshold, helping traders decide when to trade or skip a session.
Key Features
GARCH(1,1) Volatility Modeling: Uses log-transformed true ranges with exponential moving average centering
Forward-Looking Predictions: Makes predictions at session start before the day unfolds
Dynamic or Static Thresholds: Choose between fixed dollar thresholds or adaptive 20-day averages
Accuracy Tracking: Monitors prediction accuracy with overall and recent (20-day) hit rates
Visual Session Boxes: Colors trading sessions green (trade) or red (skip) based on predictions
Real-Time Statistics: Displays current predictions, thresholds, and performance metrics
How It Works
Data Transformation: Log-transforms daily true ranges and centers them using an EMA
Variance Modeling: Updates GARCH variance using: σ²ₜ = ω + α(residual²) + β(σ²ₜ₋₁)
Prediction Generation: Back-transforms log predictions to dollar values
Signal Generation: Compares predictions to threshold to generate trade/skip signals
Performance Tracking: Validates predictions against actual outcomes
Parameters
GARCH Parameters (ω, α, β): Control volatility persistence and mean reversion
EMA Period: Smoothing period for log range centering
Threshold Settings: Static dollar amount or dynamic multiplier of recent averages
Session Time: Define regular trading hours for analysis
Best Use Cases
Breakout and momentum strategies that perform better on high-range days
Risk management by avoiding low-volatility sessions
Futures day trading (optimized for MNQ/NQ detection)
Any strategy where daily range impacts profitability
Important Notes
Requires 5+ sessions for initialization and warm-up
Accuracy depends heavily on proper parameter tuning for your specific instrument
Default parameters may need adjustment for different markets
Monitor the hit rate to validate effectiveness on your timeframe
