PINE LIBRARY
PineStats
█ OVERVIEW
PineStats is a comprehensive statistical analysis library for Pine Script v6, providing 104 functions across 6 modules. Built for quantitative traders, researchers, and indicator developers who need professional-grade statistics without reinventing the wheel.
For building mean-reversion strategies, analyzing return distributions, measuring correlations, or testing for market regimes.
█ MODULES
CORE STATISTICS (20 functions)
• Central tendency: mean, median, WMA, EMA
• Dispersion: variance, stdev, MAD, range
• Standardization: z-score, robust z-score, normalize, percentile
• Distribution shape: skewness, kurtosis
PROBABILITY DISTRIBUTIONS (17 functions)
• Normal: PDF, CDF, inverse CDF (quantile function)
• Power-law: Hill estimator, MLE alpha, survival function
• Exponential: PDF, CDF, rate estimation
• Normality testing: Jarque-Bera test
ENTROPY (9 functions)
• Shannon entropy (information theory)
• Tsallis entropy (non-extensive, fat-tail sensitive)
• Permutation entropy (ordinal patterns)
• Approximate entropy (regularity measure)
• Entropy-based regime detection
PROBABILITY (21 functions)
• Win rates and expected value
• First passage time estimation
• TP/SL probability analysis
• Conditional probability and Bayes updates
• Streak and drawdown probabilities
REGRESSION (19 functions)
• Linear regression: slope, intercept, forecast
• Goodness of fit: R², adjusted R², standard error
• Statistical tests: t-statistic, p-value, significance
• Trend analysis: strength, angle, acceleration
• Quadratic regression
CORRELATION (18 functions)
• Pearson, Spearman, Kendall correlation
• Covariance, beta, alpha (Jensen's)
• Rolling correlation analysis
• Autocorrelation and cross-correlation
• Information ratio, tracking error
█ QUICK START
Pine Script®
Pine Script®
█ USE CASES
✓ Mean Reversion — z-scores, percentiles, Bollinger-style analysis
✓ Regime Detection — entropy measures, correlation regimes
✓ Risk Analysis — drawdown probability, VaR via quantiles
✓ Strategy Evaluation — expected value, win rates, R:R analysis
✓ Distribution Analysis — normality tests, fat-tail detection
✓ Multi-Asset — beta, alpha, correlation, relative strength
█ NOTES
• All functions return `na` on invalid inputs
• Designed for Pine Script v6
• Fully documented in the library header
• Part of the Pine ecosystem: PineStats, PineQuant, PineCriticality, PineWavelet
█ REFERENCES
• Abramowitz & Stegun — Normal CDF approximation
• Acklam's algorithm — Inverse normal CDF
• Hill estimator — Power-law tail estimation
• Tsallis statistics — Non-extensive entropy
Full documentation in the library header.
mean(src, length)
Calculates the arithmetic mean (simple moving average) over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Arithmetic mean of the last `length` values, or `na` if inputs invalid
wma_custom(src, length)
Calculates weighted moving average with linearly decreasing weights
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Weighted moving average, or `na` if inputs invalid
ema_custom(src, length)
Calculates exponential moving average
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Exponential moving average, or `na` if inputs invalid
median(src, length)
Calculates the median value over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Median value, or `na` if inputs invalid
variance(src, length)
Calculates population variance over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Population variance, or `na` if inputs invalid
stdev(src, length)
Calculates population standard deviation over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Population standard deviation, or `na` if inputs invalid
mad(src, length)
Calculates Median Absolute Deviation (MAD) - robust dispersion measure
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: MAD value, or `na` if inputs invalid
data_range(src, length)
Calculates the range (highest - lowest) over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Range value, or `na` if inputs invalid
zscore(src, length)
Calculates z-score (number of standard deviations from mean)
Parameters:
src (float): Source series
length (simple int): Lookback period for mean and stdev calculation (must be >= 2)
Returns: Z-score, or `na` if inputs invalid or stdev is zero
zscore_robust(src, length)
Calculates robust z-score using median and MAD (resistant to outliers)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Robust z-score, or `na` if inputs invalid or MAD is zero
normalize(src, length)
Normalizes value to [0, 1] range using min-max scaling
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Normalized value in [0, 1], or `na` if inputs invalid or range is zero
percentile(src, length)
Calculates percentile rank of current value within lookback window
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Percentile rank (0 to 100), or `na` if inputs invalid
winsorize(src, length, lower_pct, upper_pct)
Winsorizes values by clamping to percentile bounds (reduces outlier impact)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
lower_pct (simple float): Lower percentile bound (0-100, e.g., 5 for 5th percentile)
upper_pct (simple float): Upper percentile bound (0-100, e.g., 95 for 95th percentile)
Returns: Winsorized value clamped to [lower_pct, upper_pct] bounds
skewness(src, length)
Calculates sample skewness (measure of distribution asymmetry)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 3)
Returns: Skewness value (negative = left tail, positive = right tail), or `na` if invalid
kurtosis(src, length)
Calculates excess kurtosis (measure of distribution tail heaviness)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 4)
Returns: Excess kurtosis (>0 = heavy tails, <0 = light tails), or `na` if invalid
count_valid(src, length)
Counts non-na values in lookback window (useful for data quality checks)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Count of valid (non-na) values
sum(src, length)
Calculates sum over lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Sum of values, or `na` if inputs invalid
cumsum(src)
Calculates cumulative sum (running total from first bar)
Parameters:
src (float): Source series
Returns: Cumulative sum
change(src, length)
Returns the change (difference) from n bars ago
Parameters:
src (float): Source series
length (simple int): Number of bars to look back (must be >= 1)
Returns: Current value minus value from `length` bars ago
roc(src, length)
Calculates Rate of Change (percentage change from n bars ago)
Parameters:
src (float): Source series
length (simple int): Number of bars to look back (must be >= 1)
Returns: Percentage change as decimal (0.05 = 5%), or `na` if invalid
normal_pdf_standard(x)
Calculates the standard normal probability density function (PDF)
Parameters:
x (float): The value to evaluate
Returns: PDF value at x for standard normal N(0,1)
normal_pdf(x, mu, sigma)
Calculates the normal probability density function (PDF)
Parameters:
x (float): The value to evaluate
mu (float): Mean of the distribution (default: 0)
sigma (float): Standard deviation (default: 1, must be > 0)
Returns: PDF value at x for normal N(mu, sigma²)
normal_cdf_standard(x)
Calculates the standard normal cumulative distribution function (CDF)
Parameters:
x (float): The value to evaluate
Returns: Probability P(X <= x) for standard normal N(0,1)
description Uses Abramowitz & Stegun approximation (formula 7.1.26), accurate to ~1.5e-7
normal_cdf(x, mu, sigma)
Calculates the normal cumulative distribution function (CDF)
Parameters:
x (float): The value to evaluate
mu (float): Mean of the distribution (default: 0)
sigma (float): Standard deviation (default: 1, must be > 0)
Returns: Probability P(X <= x) for normal N(mu, sigma²)
normal_inv_standard(p)
Calculates the inverse standard normal CDF (quantile function)
Parameters:
p (float): Probability value (must be in (0, 1))
Returns: x such that P(X <= x) = p for standard normal N(0,1)
description Uses Acklam's algorithm, accurate to ~1.15e-9
normal_inv(p, mu, sigma)
Calculates the inverse normal CDF (quantile function)
Parameters:
p (float): Probability value (must be in (0, 1))
mu (float): Mean of the distribution
sigma (float): Standard deviation (must be > 0)
Returns: x such that P(X <= x) = p for normal N(mu, sigma²)
power_law_alpha(src, length, tail_pct)
Estimates power-law exponent (alpha) using Hill estimator
Parameters:
src (float): Source series (typically absolute returns or drawdowns)
length (simple int): Lookback period (must be >= 10 for reliable estimates)
tail_pct (simple float): Percentage of data to use for tail estimation (default: 0.1 = top 10%)
Returns: Estimated alpha (tail index), typically 2-4 for financial data
description Alpha < 2 indicates infinite variance (very heavy tails)
description Alpha < 3 indicates infinite kurtosis
description Alpha > 4 suggests near-Gaussian behavior
power_law_alpha_mle(src, length, x_min)
Estimates power-law alpha using maximum likelihood (Clauset method)
Parameters:
src (float): Source series (positive values expected)
length (simple int): Lookback period (must be >= 20)
x_min (float): Minimum threshold for power-law behavior
Returns: Estimated alpha using MLE
power_law_pdf(x, alpha, x_min)
Calculates power-law probability density (Pareto Type I)
Parameters:
x (float): Value to evaluate (must be >= x_min)
alpha (float): Power-law exponent (must be > 1)
x_min (float): Minimum value / scale parameter (must be > 0)
Returns: PDF value
power_law_survival(x, alpha, x_min)
Calculates power-law survival function P(X > x)
Parameters:
x (float): Value to evaluate (must be >= x_min)
alpha (float): Power-law exponent (must be > 1)
x_min (float): Minimum value / scale parameter (must be > 0)
Returns: Probability of exceeding x
power_law_ks(src, length, alpha, x_min)
Tests if data follows power-law using simplified Kolmogorov-Smirnov
Parameters:
src (float): Source series
length (simple int): Lookback period
alpha (float): Estimated alpha from power_law_alpha()
x_min (float): Threshold value
Returns: KS statistic (lower = better fit, typically < 0.1 for good fit)
is_power_law(src, length, tail_pct, ks_threshold)
Simple test if distribution appears to follow power-law
Parameters:
src (float): Source series
length (simple int): Lookback period
tail_pct (simple float): Tail percentage for alpha estimation
ks_threshold (simple float): Maximum KS statistic for acceptance (default: 0.1)
Returns: true if KS test suggests power-law fit
exp_pdf(x, lambda)
Calculates exponential probability density function
Parameters:
x (float): Value to evaluate (must be >= 0)
lambda (float): Rate parameter (must be > 0)
Returns: PDF value
exp_cdf(x, lambda)
Calculates exponential cumulative distribution function
Parameters:
x (float): Value to evaluate (must be >= 0)
lambda (float): Rate parameter (must be > 0)
Returns: Probability P(X <= x)
exp_lambda(src, length)
Estimates exponential rate parameter (lambda) using MLE
Parameters:
src (float): Source series (positive values)
length (simple int): Lookback period
Returns: Estimated lambda (1/mean)
jarque_bera(src, length)
Calculates Jarque-Bera test statistic for normality
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
Returns: JB statistic (higher = more deviation from normality)
description Under normality, JB ~ chi-squared(2). JB > 6 suggests non-normality at 5% level
is_normal(src, length, significance)
Tests if distribution is approximately normal
Parameters:
src (float): Source series
length (simple int): Lookback period
significance (simple float): Significance level (default: 0.05)
Returns: true if Jarque-Bera test does not reject normality
shannon_entropy(src, length, n_bins)
Calculates Shannon entropy from a probability distribution
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
n_bins (simple int): Number of histogram bins for discretization (default: 10)
Returns: Shannon entropy in bits (log base 2)
description Higher entropy = more randomness/uncertainty, lower = more predictability
shannon_entropy_norm(src, length, n_bins)
Calculates normalized Shannon entropy [0, 1]
Parameters:
src (float): Source series
length (simple int): Lookback period
n_bins (simple int): Number of histogram bins
Returns: Normalized entropy where 0 = perfectly predictable, 1 = maximum randomness
tsallis_entropy(src, length, q, n_bins)
Calculates Tsallis entropy with q-parameter
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
q (float): Entropic index (q=1 recovers Shannon entropy)
n_bins (simple int): Number of histogram bins
Returns: Tsallis entropy value
description q < 1: emphasizes rare events (fat tails)
description q = 1: equivalent to Shannon entropy
description q > 1: emphasizes common events
optimal_q(src, length)
Estimates optimal q parameter from kurtosis
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Estimated q value that best captures the distribution's tail behavior
description Uses relationship: q ≈ (5 + kurtosis) / (3 + kurtosis) for kurtosis > 0
tsallis_q_gaussian(x, q, beta)
Calculates Tsallis q-Gaussian probability density
Parameters:
x (float): Value to evaluate
q (float): Tsallis q parameter (must be < 3)
beta (float): Width parameter (inverse temperature, must be > 0)
Returns: q-Gaussian PDF value
description q=1 recovers standard Gaussian
permutation_entropy(src, length, order)
Calculates permutation entropy (ordinal pattern complexity)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 20)
order (simple int): Embedding dimension / pattern length (2-5, default: 3)
Returns: Normalized permutation entropy [0, 1]
description Measures complexity of temporal ordering patterns
description 0 = perfectly predictable sequence, 1 = random
approx_entropy(src, length, m, r)
Calculates Approximate Entropy (ApEn) - regularity measure
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 50)
m (simple int): Embedding dimension (default: 2)
r (simple float): Tolerance as fraction of stdev (default: 0.2)
Returns: Approximate entropy value (higher = more irregular/complex)
description Lower ApEn indicates more self-similarity and predictability
entropy_regime(src, length, q, n_bins)
Detects market regime based on entropy level
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
q (float): Tsallis q parameter (use optimal_q() or default 1.5)
n_bins (simple int): Number of histogram bins
Returns: Regime indicator: -1 = trending (low entropy), 0 = transition, 1 = ranging (high entropy)
entropy_risk(src, length)
Calculates entropy-based risk indicator
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
Returns: Risk score [0, 1] where 1 = maximum divergence from Gaussian 1
hit_rate(src, length)
Calculates hit rate (probability of positive outcome) over lookback
Parameters:
src (float): Source series (positive values count as hits)
length (simple int): Lookback period
Returns: Hit rate as decimal [0, 1]
hit_rate_cond(condition, length)
Calculates hit rate for custom condition over lookback
Parameters:
condition (bool): Boolean series (true = hit)
length (simple int): Lookback period
Returns: Hit rate as decimal [0, 1]
expected_value(src, length)
Calculates expected value of a series
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Expected value (mean)
expected_value_trade(win_prob, take_profit, stop_loss)
Calculates expected value for a trade with TP and SL levels
Parameters:
win_prob (float): Probability of hitting TP (0-1)
take_profit (float): Take profit in price units or %
stop_loss (float): Stop loss in price units or % (positive value)
Returns: Expected value per trade
description EV = (win_prob * TP) - ((1 - win_prob) * SL)
breakeven_winrate(take_profit, stop_loss)
Calculates breakeven win rate for given TP/SL ratio
Parameters:
take_profit (float): Take profit distance
stop_loss (float): Stop loss distance
Returns: Required win rate for breakeven (EV = 0)
reward_risk_ratio(take_profit, stop_loss)
Calculates the reward-to-risk ratio
Parameters:
take_profit (float): Take profit distance
stop_loss (float): Stop loss distance
Returns: R:R ratio
fpt_probability(src, length, target, max_bars)
Estimates probability of price reaching target within N bars
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for volatility estimation
target (float): Target move (in same units as src, e.g., % return)
max_bars (simple int): Maximum bars to consider
Returns: Probability of reaching target within max_bars
description Based on random walk with drift approximation
fpt_mean(src, length, target)
Estimates mean first passage time to target level
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for volatility estimation
target (float): Target move
Returns: Expected number of bars to reach target (can be infinite)
fpt_historical(src, length, target)
Counts historical bars to reach target from each point
Parameters:
src (float): Source series (typically price or returns)
length (simple int): Lookback period
target (float): Target move from each starting point
Returns: Array of first passage times (na if target not reached within lookback)
tp_probability(src, length, tp_distance, sl_distance)
Estimates probability of hitting TP before SL
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for estimation
tp_distance (float): Take profit distance (positive)
sl_distance (float): Stop loss distance (positive)
Returns: Probability of TP being hit first
trade_probability(src, length, tp_pct, sl_pct)
Calculates complete trade probability and EV analysis
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
tp_pct (float): Take profit percentage
sl_pct (float): Stop loss percentage
Returns: Tuple: [tp_probability, expected_value, breakeven_wr, actual_rr]
cond_prob(condition_a, condition_b, length)
Calculates conditional probability P(B|A) from historical data
Parameters:
condition_a (bool): Condition A (the given condition)
condition_b (bool): Condition B (the outcome)
length (simple int): Lookback period
Returns: P(B|A) = P(A and B) / P(A)
bayes_update(prior, likelihood, false_positive)
Updates probability using Bayes' theorem
Parameters:
prior (float): Prior probability P(H)
likelihood (float): P(E|H) - probability of evidence given hypothesis
false_positive (float): P(E|~H) - probability of evidence given hypothesis is false
Returns: Posterior probability P(H|E)
streak_prob(win_rate, streak_length)
Calculates probability of N consecutive wins given win rate
Parameters:
win_rate (float): Single-trade win probability
streak_length (simple int): Number of consecutive wins
Returns: Probability of streak
losing_streak_prob(win_rate, streak_length)
Calculates probability of experiencing N consecutive losses
Parameters:
win_rate (float): Single-trade win probability
streak_length (simple int): Number of consecutive losses
Returns: Probability of losing streak
drawdown_prob(src, length, dd_threshold)
Estimates probability of drawdown exceeding threshold
Parameters:
src (float): Source series (returns)
length (simple int): Lookback period
dd_threshold (float): Drawdown threshold (as positive decimal, e.g., 0.10 = 10%)
Returns: Historical probability of exceeding drawdown threshold
prob_to_odds(prob)
Calculates odds from probability
Parameters:
prob (float): Probability (0-1)
Returns: Odds (prob / (1 - prob))
odds_to_prob(odds)
Calculates probability from odds
Parameters:
odds (float): Odds ratio
Returns: Probability (0-1)
implied_prob(decimal_odds)
Calculates implied probability from decimal odds (betting)
Parameters:
decimal_odds (float): Decimal odds (e.g., 2.5 means $2.50 return per $1 bet)
Returns: Implied probability
logit(prob)
Calculates log-odds (logit) from probability
Parameters:
prob (float): Probability (must be in (0, 1))
Returns: Log-odds
inv_logit(log_odds)
Calculates probability from log-odds (inverse logit / sigmoid)
Parameters:
log_odds (float): Log-odds value
Returns: Probability (0-1)
linreg_slope(src, length)
Calculates linear regression slope
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Slope coefficient (change per bar)
linreg_intercept(src, length)
Calculates linear regression intercept
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Intercept (predicted value at oldest bar in window)
linreg_value(src, length)
Calculates predicted value at current bar using linear regression
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Predicted value at current bar (end of regression line)
linreg_forecast(src, length, offset)
Forecasts value N bars ahead using linear regression
Parameters:
src (float): Source series
length (simple int): Lookback period for regression
offset (simple int): Bars ahead to forecast (positive = future)
Returns: Forecasted value
linreg_channel(src, length, mult)
Calculates linear regression channel with bands
Parameters:
src (float): Source series
length (simple int): Lookback period
mult (simple float): Standard deviation multiplier for bands
Returns: Tuple: [center, upper, lower]
r_squared(src, length)
Calculates R-squared (coefficient of determination)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: R² value [0, 1] where 1 = perfect linear fit
adj_r_squared(src, length)
Calculates adjusted R-squared (accounts for sample size)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Adjusted R² value
std_error(src, length)
Calculates standard error of estimate (residual standard deviation)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Standard error
residual(src, length)
Calculates residual at current bar
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Residual (actual - predicted)
residuals(src, length)
Returns array of all residuals in lookback window
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Array of residuals
t_statistic(src, length)
Calculates t-statistic for slope coefficient
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: T-statistic (slope / standard error of slope)
slope_pvalue(src, length)
Approximates p-value for slope t-test (two-tailed)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Approximate p-value
is_significant(src, length, alpha)
Tests if regression slope is statistically significant
Parameters:
src (float): Source series
length (simple int): Lookback period
alpha (simple float): Significance level (default: 0.05)
Returns: true if slope is significant at alpha level
trend_strength(src, length)
Calculates normalized trend strength based on R² and slope
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Trend strength [-1, 1] where sign indicates direction
trend_angle(src, length)
Calculates trend angle in degrees
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Angle in degrees (positive = uptrend, negative = downtrend)
linreg_acceleration(src, length)
Calculates trend acceleration (second derivative)
Parameters:
src (float): Source series
length (simple int): Lookback period for each regression
Returns: Acceleration (change in slope)
linreg_deviation(src, length)
Calculates deviation from regression line in standard error units
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Deviation in standard error units (like z-score)
quadreg_coefficients(src, length)
Fits quadratic regression and returns coefficients
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 4)
Returns: Tuple: [a, b, c] for y = a*x² + b*x + c
quadreg_value(src, length)
Calculates quadratic regression value at current bar
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Predicted value from quadratic fit
correlation(x, y, length)
Calculates Pearson correlation coefficient between two series
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Correlation coefficient [-1, 1]
covariance(x, y, length)
Calculates sample covariance between two series
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 2)
Returns: Covariance value
beta(asset, benchmark, length)
Calculates beta coefficient (slope of regression of y on x)
Parameters:
asset (float): Asset returns series
benchmark (float): Benchmark returns series
length (simple int): Lookback period
Returns: Beta coefficient
description Beta = Cov(asset, benchmark) / Var(benchmark)
alpha(asset, benchmark, length, risk_free)
Calculates alpha (Jensen's alpha / intercept)
Parameters:
asset (float): Asset returns series
benchmark (float): Benchmark returns series
length (simple int): Lookback period
risk_free (float): Risk-free rate (default: 0)
Returns: Alpha value (excess return not explained by beta)
spearman(x, y, length)
Calculates Spearman rank correlation coefficient
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Spearman correlation [-1, 1]
description More robust to outliers than Pearson correlation
kendall_tau(x, y, length)
Calculates Kendall's tau rank correlation (simplified)
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Kendall's tau [-1, 1]
correlation_change(x, y, length, change_period)
Calculates change in correlation over time
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period for correlation
change_period (simple int): Period over which to measure change
Returns: Change in correlation
correlation_regime(x, y, length, ma_length)
Detects correlation regime based on level and stability
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period for correlation
ma_length (simple int): Moving average length for smoothing
Returns: Regime: -1 = negative, 0 = uncorrelated, 1 = positive
correlation_stability(x, y, length, stability_length)
Calculates correlation stability (inverse of volatility)
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback for correlation
stability_length (simple int): Lookback for stability calculation
Returns: Stability score [0, 1] where 1 = perfectly stable
relative_strength(asset, benchmark, length)
Calculates relative strength of asset vs benchmark
Parameters:
asset (float): Asset price series
benchmark (float): Benchmark price series
length (simple int): Smoothing period
Returns: Relative strength ratio (normalized)
tracking_error(asset, benchmark, length)
Calculates tracking error (standard deviation of excess returns)
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
Returns: Tracking error (annualize by multiplying by sqrt(252) for daily data)
information_ratio(asset, benchmark, length)
Calculates information ratio (risk-adjusted excess return)
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
Returns: Information ratio
capture_ratio(asset, benchmark, length, up_capture)
Calculates up/down capture ratio
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
up_capture (simple bool): If true, calculate up capture; if false, down capture
Returns: Capture ratio
autocorrelation(src, length, lag)
Calculates autocorrelation at specified lag
Parameters:
src (float): Source series
length (simple int): Lookback period
lag (simple int): Lag for autocorrelation (default: 1)
Returns: Autocorrelation at specified lag
partial_autocorr(src, length)
Calculates partial autocorrelation at lag 1
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: PACF at lag 1 (equals ACF at lag 1)
autocorr_test(src, length, max_lag)
Tests for significant autocorrelation (Ljung-Box inspired)
Parameters:
src (float): Source series
length (simple int): Lookback period
max_lag (simple int): Maximum lag to test
Returns: Sum of squared autocorrelations (higher = more autocorrelation)
cross_correlation(x, y, length, lag)
Calculates cross-correlation at specified lag
Parameters:
x (float): First series
y (float): Second series (lagged)
length (simple int): Lookback period
lag (simple int): Lag to apply to y (positive = y leads x)
Returns: Cross-correlation at specified lag
cross_correlation_peak(x, y, length, max_lag)
Finds lag with maximum cross-correlation
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period
max_lag (simple int): Maximum lag to search (both directions)
Returns: Tuple: [best_lag, max_correlation]
PineStats is a comprehensive statistical analysis library for Pine Script v6, providing 104 functions across 6 modules. Built for quantitative traders, researchers, and indicator developers who need professional-grade statistics without reinventing the wheel.
For building mean-reversion strategies, analyzing return distributions, measuring correlations, or testing for market regimes.
█ MODULES
CORE STATISTICS (20 functions)
• Central tendency: mean, median, WMA, EMA
• Dispersion: variance, stdev, MAD, range
• Standardization: z-score, robust z-score, normalize, percentile
• Distribution shape: skewness, kurtosis
PROBABILITY DISTRIBUTIONS (17 functions)
• Normal: PDF, CDF, inverse CDF (quantile function)
• Power-law: Hill estimator, MLE alpha, survival function
• Exponential: PDF, CDF, rate estimation
• Normality testing: Jarque-Bera test
ENTROPY (9 functions)
• Shannon entropy (information theory)
• Tsallis entropy (non-extensive, fat-tail sensitive)
• Permutation entropy (ordinal patterns)
• Approximate entropy (regularity measure)
• Entropy-based regime detection
PROBABILITY (21 functions)
• Win rates and expected value
• First passage time estimation
• TP/SL probability analysis
• Conditional probability and Bayes updates
• Streak and drawdown probabilities
REGRESSION (19 functions)
• Linear regression: slope, intercept, forecast
• Goodness of fit: R², adjusted R², standard error
• Statistical tests: t-statistic, p-value, significance
• Trend analysis: strength, angle, acceleration
• Quadratic regression
CORRELATION (18 functions)
• Pearson, Spearman, Kendall correlation
• Covariance, beta, alpha (Jensen's)
• Rolling correlation analysis
• Autocorrelation and cross-correlation
• Information ratio, tracking error
█ QUICK START
import HenriqueCentieiro/PineStats/1 as stats
// Z-score for mean reversion
z = stats.zscore(close, 20)
// Test if returns are normally distributed
returns = (close - close[1]) / close[1]
isGaussian = stats.is_normal(returns, 100, 0.05)
// Regression channel
[center, upper, lower] = stats.linreg_channel(close, 50, 2.0)
// Correlation with benchmark
spyReturns = request.security("SPY", timeframe.period, close/close[1] - 1)
beta = stats.beta(returns, spyReturns, 60)
█ USE CASES
✓ Mean Reversion — z-scores, percentiles, Bollinger-style analysis
✓ Regime Detection — entropy measures, correlation regimes
✓ Risk Analysis — drawdown probability, VaR via quantiles
✓ Strategy Evaluation — expected value, win rates, R:R analysis
✓ Distribution Analysis — normality tests, fat-tail detection
✓ Multi-Asset — beta, alpha, correlation, relative strength
█ NOTES
• All functions return `na` on invalid inputs
• Designed for Pine Script v6
• Fully documented in the library header
• Part of the Pine ecosystem: PineStats, PineQuant, PineCriticality, PineWavelet
█ REFERENCES
• Abramowitz & Stegun — Normal CDF approximation
• Acklam's algorithm — Inverse normal CDF
• Hill estimator — Power-law tail estimation
• Tsallis statistics — Non-extensive entropy
Full documentation in the library header.
mean(src, length)
Calculates the arithmetic mean (simple moving average) over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Arithmetic mean of the last `length` values, or `na` if inputs invalid
wma_custom(src, length)
Calculates weighted moving average with linearly decreasing weights
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Weighted moving average, or `na` if inputs invalid
ema_custom(src, length)
Calculates exponential moving average
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Exponential moving average, or `na` if inputs invalid
median(src, length)
Calculates the median value over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Median value, or `na` if inputs invalid
variance(src, length)
Calculates population variance over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Population variance, or `na` if inputs invalid
stdev(src, length)
Calculates population standard deviation over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Population standard deviation, or `na` if inputs invalid
mad(src, length)
Calculates Median Absolute Deviation (MAD) - robust dispersion measure
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: MAD value, or `na` if inputs invalid
data_range(src, length)
Calculates the range (highest - lowest) over a lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Range value, or `na` if inputs invalid
zscore(src, length)
Calculates z-score (number of standard deviations from mean)
Parameters:
src (float): Source series
length (simple int): Lookback period for mean and stdev calculation (must be >= 2)
Returns: Z-score, or `na` if inputs invalid or stdev is zero
zscore_robust(src, length)
Calculates robust z-score using median and MAD (resistant to outliers)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Robust z-score, or `na` if inputs invalid or MAD is zero
normalize(src, length)
Normalizes value to [0, 1] range using min-max scaling
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Normalized value in [0, 1], or `na` if inputs invalid or range is zero
percentile(src, length)
Calculates percentile rank of current value within lookback window
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Percentile rank (0 to 100), or `na` if inputs invalid
winsorize(src, length, lower_pct, upper_pct)
Winsorizes values by clamping to percentile bounds (reduces outlier impact)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
lower_pct (simple float): Lower percentile bound (0-100, e.g., 5 for 5th percentile)
upper_pct (simple float): Upper percentile bound (0-100, e.g., 95 for 95th percentile)
Returns: Winsorized value clamped to [lower_pct, upper_pct] bounds
skewness(src, length)
Calculates sample skewness (measure of distribution asymmetry)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 3)
Returns: Skewness value (negative = left tail, positive = right tail), or `na` if invalid
kurtosis(src, length)
Calculates excess kurtosis (measure of distribution tail heaviness)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 4)
Returns: Excess kurtosis (>0 = heavy tails, <0 = light tails), or `na` if invalid
count_valid(src, length)
Counts non-na values in lookback window (useful for data quality checks)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Count of valid (non-na) values
sum(src, length)
Calculates sum over lookback period
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 1)
Returns: Sum of values, or `na` if inputs invalid
cumsum(src)
Calculates cumulative sum (running total from first bar)
Parameters:
src (float): Source series
Returns: Cumulative sum
change(src, length)
Returns the change (difference) from n bars ago
Parameters:
src (float): Source series
length (simple int): Number of bars to look back (must be >= 1)
Returns: Current value minus value from `length` bars ago
roc(src, length)
Calculates Rate of Change (percentage change from n bars ago)
Parameters:
src (float): Source series
length (simple int): Number of bars to look back (must be >= 1)
Returns: Percentage change as decimal (0.05 = 5%), or `na` if invalid
normal_pdf_standard(x)
Calculates the standard normal probability density function (PDF)
Parameters:
x (float): The value to evaluate
Returns: PDF value at x for standard normal N(0,1)
normal_pdf(x, mu, sigma)
Calculates the normal probability density function (PDF)
Parameters:
x (float): The value to evaluate
mu (float): Mean of the distribution (default: 0)
sigma (float): Standard deviation (default: 1, must be > 0)
Returns: PDF value at x for normal N(mu, sigma²)
normal_cdf_standard(x)
Calculates the standard normal cumulative distribution function (CDF)
Parameters:
x (float): The value to evaluate
Returns: Probability P(X <= x) for standard normal N(0,1)
description Uses Abramowitz & Stegun approximation (formula 7.1.26), accurate to ~1.5e-7
normal_cdf(x, mu, sigma)
Calculates the normal cumulative distribution function (CDF)
Parameters:
x (float): The value to evaluate
mu (float): Mean of the distribution (default: 0)
sigma (float): Standard deviation (default: 1, must be > 0)
Returns: Probability P(X <= x) for normal N(mu, sigma²)
normal_inv_standard(p)
Calculates the inverse standard normal CDF (quantile function)
Parameters:
p (float): Probability value (must be in (0, 1))
Returns: x such that P(X <= x) = p for standard normal N(0,1)
description Uses Acklam's algorithm, accurate to ~1.15e-9
normal_inv(p, mu, sigma)
Calculates the inverse normal CDF (quantile function)
Parameters:
p (float): Probability value (must be in (0, 1))
mu (float): Mean of the distribution
sigma (float): Standard deviation (must be > 0)
Returns: x such that P(X <= x) = p for normal N(mu, sigma²)
power_law_alpha(src, length, tail_pct)
Estimates power-law exponent (alpha) using Hill estimator
Parameters:
src (float): Source series (typically absolute returns or drawdowns)
length (simple int): Lookback period (must be >= 10 for reliable estimates)
tail_pct (simple float): Percentage of data to use for tail estimation (default: 0.1 = top 10%)
Returns: Estimated alpha (tail index), typically 2-4 for financial data
description Alpha < 2 indicates infinite variance (very heavy tails)
description Alpha < 3 indicates infinite kurtosis
description Alpha > 4 suggests near-Gaussian behavior
power_law_alpha_mle(src, length, x_min)
Estimates power-law alpha using maximum likelihood (Clauset method)
Parameters:
src (float): Source series (positive values expected)
length (simple int): Lookback period (must be >= 20)
x_min (float): Minimum threshold for power-law behavior
Returns: Estimated alpha using MLE
power_law_pdf(x, alpha, x_min)
Calculates power-law probability density (Pareto Type I)
Parameters:
x (float): Value to evaluate (must be >= x_min)
alpha (float): Power-law exponent (must be > 1)
x_min (float): Minimum value / scale parameter (must be > 0)
Returns: PDF value
power_law_survival(x, alpha, x_min)
Calculates power-law survival function P(X > x)
Parameters:
x (float): Value to evaluate (must be >= x_min)
alpha (float): Power-law exponent (must be > 1)
x_min (float): Minimum value / scale parameter (must be > 0)
Returns: Probability of exceeding x
power_law_ks(src, length, alpha, x_min)
Tests if data follows power-law using simplified Kolmogorov-Smirnov
Parameters:
src (float): Source series
length (simple int): Lookback period
alpha (float): Estimated alpha from power_law_alpha()
x_min (float): Threshold value
Returns: KS statistic (lower = better fit, typically < 0.1 for good fit)
is_power_law(src, length, tail_pct, ks_threshold)
Simple test if distribution appears to follow power-law
Parameters:
src (float): Source series
length (simple int): Lookback period
tail_pct (simple float): Tail percentage for alpha estimation
ks_threshold (simple float): Maximum KS statistic for acceptance (default: 0.1)
Returns: true if KS test suggests power-law fit
exp_pdf(x, lambda)
Calculates exponential probability density function
Parameters:
x (float): Value to evaluate (must be >= 0)
lambda (float): Rate parameter (must be > 0)
Returns: PDF value
exp_cdf(x, lambda)
Calculates exponential cumulative distribution function
Parameters:
x (float): Value to evaluate (must be >= 0)
lambda (float): Rate parameter (must be > 0)
Returns: Probability P(X <= x)
exp_lambda(src, length)
Estimates exponential rate parameter (lambda) using MLE
Parameters:
src (float): Source series (positive values)
length (simple int): Lookback period
Returns: Estimated lambda (1/mean)
jarque_bera(src, length)
Calculates Jarque-Bera test statistic for normality
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
Returns: JB statistic (higher = more deviation from normality)
description Under normality, JB ~ chi-squared(2). JB > 6 suggests non-normality at 5% level
is_normal(src, length, significance)
Tests if distribution is approximately normal
Parameters:
src (float): Source series
length (simple int): Lookback period
significance (simple float): Significance level (default: 0.05)
Returns: true if Jarque-Bera test does not reject normality
shannon_entropy(src, length, n_bins)
Calculates Shannon entropy from a probability distribution
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
n_bins (simple int): Number of histogram bins for discretization (default: 10)
Returns: Shannon entropy in bits (log base 2)
description Higher entropy = more randomness/uncertainty, lower = more predictability
shannon_entropy_norm(src, length, n_bins)
Calculates normalized Shannon entropy [0, 1]
Parameters:
src (float): Source series
length (simple int): Lookback period
n_bins (simple int): Number of histogram bins
Returns: Normalized entropy where 0 = perfectly predictable, 1 = maximum randomness
tsallis_entropy(src, length, q, n_bins)
Calculates Tsallis entropy with q-parameter
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 10)
q (float): Entropic index (q=1 recovers Shannon entropy)
n_bins (simple int): Number of histogram bins
Returns: Tsallis entropy value
description q < 1: emphasizes rare events (fat tails)
description q = 1: equivalent to Shannon entropy
description q > 1: emphasizes common events
optimal_q(src, length)
Estimates optimal q parameter from kurtosis
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Estimated q value that best captures the distribution's tail behavior
description Uses relationship: q ≈ (5 + kurtosis) / (3 + kurtosis) for kurtosis > 0
tsallis_q_gaussian(x, q, beta)
Calculates Tsallis q-Gaussian probability density
Parameters:
x (float): Value to evaluate
q (float): Tsallis q parameter (must be < 3)
beta (float): Width parameter (inverse temperature, must be > 0)
Returns: q-Gaussian PDF value
description q=1 recovers standard Gaussian
permutation_entropy(src, length, order)
Calculates permutation entropy (ordinal pattern complexity)
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 20)
order (simple int): Embedding dimension / pattern length (2-5, default: 3)
Returns: Normalized permutation entropy [0, 1]
description Measures complexity of temporal ordering patterns
description 0 = perfectly predictable sequence, 1 = random
approx_entropy(src, length, m, r)
Calculates Approximate Entropy (ApEn) - regularity measure
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 50)
m (simple int): Embedding dimension (default: 2)
r (simple float): Tolerance as fraction of stdev (default: 0.2)
Returns: Approximate entropy value (higher = more irregular/complex)
description Lower ApEn indicates more self-similarity and predictability
entropy_regime(src, length, q, n_bins)
Detects market regime based on entropy level
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
q (float): Tsallis q parameter (use optimal_q() or default 1.5)
n_bins (simple int): Number of histogram bins
Returns: Regime indicator: -1 = trending (low entropy), 0 = transition, 1 = ranging (high entropy)
entropy_risk(src, length)
Calculates entropy-based risk indicator
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
Returns: Risk score [0, 1] where 1 = maximum divergence from Gaussian 1
hit_rate(src, length)
Calculates hit rate (probability of positive outcome) over lookback
Parameters:
src (float): Source series (positive values count as hits)
length (simple int): Lookback period
Returns: Hit rate as decimal [0, 1]
hit_rate_cond(condition, length)
Calculates hit rate for custom condition over lookback
Parameters:
condition (bool): Boolean series (true = hit)
length (simple int): Lookback period
Returns: Hit rate as decimal [0, 1]
expected_value(src, length)
Calculates expected value of a series
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Expected value (mean)
expected_value_trade(win_prob, take_profit, stop_loss)
Calculates expected value for a trade with TP and SL levels
Parameters:
win_prob (float): Probability of hitting TP (0-1)
take_profit (float): Take profit in price units or %
stop_loss (float): Stop loss in price units or % (positive value)
Returns: Expected value per trade
description EV = (win_prob * TP) - ((1 - win_prob) * SL)
breakeven_winrate(take_profit, stop_loss)
Calculates breakeven win rate for given TP/SL ratio
Parameters:
take_profit (float): Take profit distance
stop_loss (float): Stop loss distance
Returns: Required win rate for breakeven (EV = 0)
reward_risk_ratio(take_profit, stop_loss)
Calculates the reward-to-risk ratio
Parameters:
take_profit (float): Take profit distance
stop_loss (float): Stop loss distance
Returns: R:R ratio
fpt_probability(src, length, target, max_bars)
Estimates probability of price reaching target within N bars
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for volatility estimation
target (float): Target move (in same units as src, e.g., % return)
max_bars (simple int): Maximum bars to consider
Returns: Probability of reaching target within max_bars
description Based on random walk with drift approximation
fpt_mean(src, length, target)
Estimates mean first passage time to target level
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for volatility estimation
target (float): Target move
Returns: Expected number of bars to reach target (can be infinite)
fpt_historical(src, length, target)
Counts historical bars to reach target from each point
Parameters:
src (float): Source series (typically price or returns)
length (simple int): Lookback period
target (float): Target move from each starting point
Returns: Array of first passage times (na if target not reached within lookback)
tp_probability(src, length, tp_distance, sl_distance)
Estimates probability of hitting TP before SL
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback for estimation
tp_distance (float): Take profit distance (positive)
sl_distance (float): Stop loss distance (positive)
Returns: Probability of TP being hit first
trade_probability(src, length, tp_pct, sl_pct)
Calculates complete trade probability and EV analysis
Parameters:
src (float): Source series (typically returns)
length (simple int): Lookback period
tp_pct (float): Take profit percentage
sl_pct (float): Stop loss percentage
Returns: Tuple: [tp_probability, expected_value, breakeven_wr, actual_rr]
cond_prob(condition_a, condition_b, length)
Calculates conditional probability P(B|A) from historical data
Parameters:
condition_a (bool): Condition A (the given condition)
condition_b (bool): Condition B (the outcome)
length (simple int): Lookback period
Returns: P(B|A) = P(A and B) / P(A)
bayes_update(prior, likelihood, false_positive)
Updates probability using Bayes' theorem
Parameters:
prior (float): Prior probability P(H)
likelihood (float): P(E|H) - probability of evidence given hypothesis
false_positive (float): P(E|~H) - probability of evidence given hypothesis is false
Returns: Posterior probability P(H|E)
streak_prob(win_rate, streak_length)
Calculates probability of N consecutive wins given win rate
Parameters:
win_rate (float): Single-trade win probability
streak_length (simple int): Number of consecutive wins
Returns: Probability of streak
losing_streak_prob(win_rate, streak_length)
Calculates probability of experiencing N consecutive losses
Parameters:
win_rate (float): Single-trade win probability
streak_length (simple int): Number of consecutive losses
Returns: Probability of losing streak
drawdown_prob(src, length, dd_threshold)
Estimates probability of drawdown exceeding threshold
Parameters:
src (float): Source series (returns)
length (simple int): Lookback period
dd_threshold (float): Drawdown threshold (as positive decimal, e.g., 0.10 = 10%)
Returns: Historical probability of exceeding drawdown threshold
prob_to_odds(prob)
Calculates odds from probability
Parameters:
prob (float): Probability (0-1)
Returns: Odds (prob / (1 - prob))
odds_to_prob(odds)
Calculates probability from odds
Parameters:
odds (float): Odds ratio
Returns: Probability (0-1)
implied_prob(decimal_odds)
Calculates implied probability from decimal odds (betting)
Parameters:
decimal_odds (float): Decimal odds (e.g., 2.5 means $2.50 return per $1 bet)
Returns: Implied probability
logit(prob)
Calculates log-odds (logit) from probability
Parameters:
prob (float): Probability (must be in (0, 1))
Returns: Log-odds
inv_logit(log_odds)
Calculates probability from log-odds (inverse logit / sigmoid)
Parameters:
log_odds (float): Log-odds value
Returns: Probability (0-1)
linreg_slope(src, length)
Calculates linear regression slope
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Slope coefficient (change per bar)
linreg_intercept(src, length)
Calculates linear regression intercept
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 2)
Returns: Intercept (predicted value at oldest bar in window)
linreg_value(src, length)
Calculates predicted value at current bar using linear regression
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Predicted value at current bar (end of regression line)
linreg_forecast(src, length, offset)
Forecasts value N bars ahead using linear regression
Parameters:
src (float): Source series
length (simple int): Lookback period for regression
offset (simple int): Bars ahead to forecast (positive = future)
Returns: Forecasted value
linreg_channel(src, length, mult)
Calculates linear regression channel with bands
Parameters:
src (float): Source series
length (simple int): Lookback period
mult (simple float): Standard deviation multiplier for bands
Returns: Tuple: [center, upper, lower]
r_squared(src, length)
Calculates R-squared (coefficient of determination)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: R² value [0, 1] where 1 = perfect linear fit
adj_r_squared(src, length)
Calculates adjusted R-squared (accounts for sample size)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Adjusted R² value
std_error(src, length)
Calculates standard error of estimate (residual standard deviation)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Standard error
residual(src, length)
Calculates residual at current bar
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Residual (actual - predicted)
residuals(src, length)
Returns array of all residuals in lookback window
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Array of residuals
t_statistic(src, length)
Calculates t-statistic for slope coefficient
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: T-statistic (slope / standard error of slope)
slope_pvalue(src, length)
Approximates p-value for slope t-test (two-tailed)
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Approximate p-value
is_significant(src, length, alpha)
Tests if regression slope is statistically significant
Parameters:
src (float): Source series
length (simple int): Lookback period
alpha (simple float): Significance level (default: 0.05)
Returns: true if slope is significant at alpha level
trend_strength(src, length)
Calculates normalized trend strength based on R² and slope
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Trend strength [-1, 1] where sign indicates direction
trend_angle(src, length)
Calculates trend angle in degrees
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Angle in degrees (positive = uptrend, negative = downtrend)
linreg_acceleration(src, length)
Calculates trend acceleration (second derivative)
Parameters:
src (float): Source series
length (simple int): Lookback period for each regression
Returns: Acceleration (change in slope)
linreg_deviation(src, length)
Calculates deviation from regression line in standard error units
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Deviation in standard error units (like z-score)
quadreg_coefficients(src, length)
Fits quadratic regression and returns coefficients
Parameters:
src (float): Source series
length (simple int): Lookback period (must be >= 4)
Returns: Tuple: [a, b, c] for y = a*x² + b*x + c
quadreg_value(src, length)
Calculates quadratic regression value at current bar
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: Predicted value from quadratic fit
correlation(x, y, length)
Calculates Pearson correlation coefficient between two series
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Correlation coefficient [-1, 1]
covariance(x, y, length)
Calculates sample covariance between two series
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 2)
Returns: Covariance value
beta(asset, benchmark, length)
Calculates beta coefficient (slope of regression of y on x)
Parameters:
asset (float): Asset returns series
benchmark (float): Benchmark returns series
length (simple int): Lookback period
Returns: Beta coefficient
description Beta = Cov(asset, benchmark) / Var(benchmark)
alpha(asset, benchmark, length, risk_free)
Calculates alpha (Jensen's alpha / intercept)
Parameters:
asset (float): Asset returns series
benchmark (float): Benchmark returns series
length (simple int): Lookback period
risk_free (float): Risk-free rate (default: 0)
Returns: Alpha value (excess return not explained by beta)
spearman(x, y, length)
Calculates Spearman rank correlation coefficient
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Spearman correlation [-1, 1]
description More robust to outliers than Pearson correlation
kendall_tau(x, y, length)
Calculates Kendall's tau rank correlation (simplified)
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period (must be >= 3)
Returns: Kendall's tau [-1, 1]
correlation_change(x, y, length, change_period)
Calculates change in correlation over time
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period for correlation
change_period (simple int): Period over which to measure change
Returns: Change in correlation
correlation_regime(x, y, length, ma_length)
Detects correlation regime based on level and stability
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period for correlation
ma_length (simple int): Moving average length for smoothing
Returns: Regime: -1 = negative, 0 = uncorrelated, 1 = positive
correlation_stability(x, y, length, stability_length)
Calculates correlation stability (inverse of volatility)
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback for correlation
stability_length (simple int): Lookback for stability calculation
Returns: Stability score [0, 1] where 1 = perfectly stable
relative_strength(asset, benchmark, length)
Calculates relative strength of asset vs benchmark
Parameters:
asset (float): Asset price series
benchmark (float): Benchmark price series
length (simple int): Smoothing period
Returns: Relative strength ratio (normalized)
tracking_error(asset, benchmark, length)
Calculates tracking error (standard deviation of excess returns)
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
Returns: Tracking error (annualize by multiplying by sqrt(252) for daily data)
information_ratio(asset, benchmark, length)
Calculates information ratio (risk-adjusted excess return)
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
Returns: Information ratio
capture_ratio(asset, benchmark, length, up_capture)
Calculates up/down capture ratio
Parameters:
asset (float): Asset returns
benchmark (float): Benchmark returns
length (simple int): Lookback period
up_capture (simple bool): If true, calculate up capture; if false, down capture
Returns: Capture ratio
autocorrelation(src, length, lag)
Calculates autocorrelation at specified lag
Parameters:
src (float): Source series
length (simple int): Lookback period
lag (simple int): Lag for autocorrelation (default: 1)
Returns: Autocorrelation at specified lag
partial_autocorr(src, length)
Calculates partial autocorrelation at lag 1
Parameters:
src (float): Source series
length (simple int): Lookback period
Returns: PACF at lag 1 (equals ACF at lag 1)
autocorr_test(src, length, max_lag)
Tests for significant autocorrelation (Ljung-Box inspired)
Parameters:
src (float): Source series
length (simple int): Lookback period
max_lag (simple int): Maximum lag to test
Returns: Sum of squared autocorrelations (higher = more autocorrelation)
cross_correlation(x, y, length, lag)
Calculates cross-correlation at specified lag
Parameters:
x (float): First series
y (float): Second series (lagged)
length (simple int): Lookback period
lag (simple int): Lag to apply to y (positive = y leads x)
Returns: Cross-correlation at specified lag
cross_correlation_peak(x, y, length, max_lag)
Finds lag with maximum cross-correlation
Parameters:
x (float): First series
y (float): Second series
length (simple int): Lookback period
max_lag (simple int): Maximum lag to search (both directions)
Returns: Tuple: [best_lag, max_correlation]
ספריית Pine
ברוח האמיתית של TradingView, המחבר לפרסם את הקוד של Pine הזה כספרייה בקוד פתוח, כך שמתכנתים אחרים בקהילתנו יעשו שימוש חוזר. כל הכבוד למחבר! ניתן להשתמש בספרייה הזו באופן פרטי או בומים בקוד פתוח, אך השימוש בחוזר בקוד הזה בפרסומים כפוף ל-כללי הבית.
כתב ויתור
המידע והפרסומים אינם מיועדים להיות, ואינם מהווים, ייעוץ או המלצה פיננסית, השקעתית, מסחרית או מכל סוג אחר המסופקת או מאושרת על ידי TradingView. קרא עוד ב־תנאי השימוש.
ספריית Pine
ברוח האמיתית של TradingView, המחבר לפרסם את הקוד של Pine הזה כספרייה בקוד פתוח, כך שמתכנתים אחרים בקהילתנו יעשו שימוש חוזר. כל הכבוד למחבר! ניתן להשתמש בספרייה הזו באופן פרטי או בומים בקוד פתוח, אך השימוש בחוזר בקוד הזה בפרסומים כפוף ל-כללי הבית.
כתב ויתור
המידע והפרסומים אינם מיועדים להיות, ואינם מהווים, ייעוץ או המלצה פיננסית, השקעתית, מסחרית או מכל סוג אחר המסופקת או מאושרת על ידי TradingView. קרא עוד ב־תנאי השימוש.