mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
b3a64f18fa
- Added Ztest class to compute the one-sample t-statistic using sample standard deviation with Bessel correction. - Implemented validation tests for Ztest to ensure accuracy against manual calculations and PineScript. - Updated documentation for Ztest, detailing its mathematical foundation, performance profile, and common pitfalls. - Adjusted NDepend badges to reflect changes in code metrics after implementation. - Updated missing indicators report to reflect the completion of statistical indicators, including ZTEST.
39 lines
3.5 KiB
Markdown
39 lines
3.5 KiB
Markdown
# Statistics
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> "All models are wrong, but some are useful." — George Box
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Statistical tools applied to price and returns. These indicators quantify relationships, measure dispersion, test hypotheses. Unlike momentum or trend indicators, statistics describe the data itself.
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| Indicator | Full Name | Description |
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| :--- | :--- | :--- |
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| [ACF](acf/Acf.md) | Autocorrelation Function | Correlation of time series with lagged copy. For ARMA model identification. |
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| [BETA](beta/Beta.md) | Beta Coefficient | Asset volatility relative to market. β=1 means market-matched risk. |
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| [BIAS](bias/Bias.md) | Bias | Percentage deviation from moving average. Measures overextension. |
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| [CMA](cma/Cma.md) | Cumulative Moving Average | Running average of all values. Welford's algorithm. No window. |
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| [COINTEGRATION](cointegration/Cointegration.md) | Cointegration | Tests if series share long-term equilibrium. Pairs trading foundation. |
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| [CORRELATION](correlation/Correlation.md) | Correlation | Linear relationship between two variables. Range: -1 to +1. |
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| [COVARIANCE](covariance/Covariance.md) | Covariance | Joint variability of two random variables. Building block for β. |
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| [ENTROPY](entropy/Entropy.md) | Shannon Entropy | Measures uncertainty/randomness. Higher entropy = less predictable. |
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| [GEOMEAN](geomean/Geomean.md) | Geometric Mean | nth root of product. Use for growth rates and ratios. |
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| [GRANGER](granger/Granger.md) | Granger Causality | Tests if one series helps predict another. Not true causality. |
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| [HARMEAN](harmean/Harmean.md) | Harmonic Mean | Reciprocal of arithmetic mean of reciprocals. For rates/ratios. |
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| [HURST](hurst/Hurst.md) | Hurst Exponent | Long-term memory. H>0.5: trending. H<0.5: mean-reverting. |
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| [IQR](iqr/Iqr.md) | Interquartile Range | P75 - P25. Robust dispersion measure. |
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| [JB](jb/Jb.md) | Jarque-Bera Test | Normality test using skewness and kurtosis. |
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| [KENDALL](kendall/Kendall.md) | Kendall Rank Correlation | Ordinal association. Robust to outliers. |
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| [KURTOSIS](kurtosis/Kurtosis.md) | Kurtosis | Tail heaviness. High kurtosis = fat tails = more extreme events. |
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| [LINREG](linreg/LinReg.md) | Linear Regression | Least squares fit. Outputs slope, intercept, R². |
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| [MEDIAN](median/Median.md) | Median | Middle value in sorted window. Robust to outliers. |
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| [MODE](mode/Mode.md) | Mode | Most frequent value. Use for categorical or discrete data. |
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| [PACF](pacf/Pacf.md) | Partial Autocorrelation Function | Direct correlation at lag k after removing intermediate effects. For AR model identification. |
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| [PERCENTILE](percentile/Percentile.md) | Percentile | Value below which given percentage of observations fall. |
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| [QUANTILE](quantile/Quantile.md) | Quantile | Divides distribution into equal probability intervals. |
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| [SKEW](skew/Skew.md) | Skewness | Distribution asymmetry. Positive: right tail. Negative: left tail. |
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| [SPEARMAN](spearman/Spearman.md) | Spearman Rank Correlation | Pearson on ranks. Measures monotonic relationship. |
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| [STDDEV](stddev/StdDev.md) | Standard Deviation | Square root of variance. Same units as data. |
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| [SUM](sum/Sum.md) | Rolling Sum | Kahan-Babuška summation. Numerically stable. |
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| [THEIL](theil/Theil.md) | Theil Index | Inequality measure. Decomposable into within/between group. |
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| [VARIANCE](variance/Variance.md) | Variance | Average squared deviation from mean. Units are squared. |
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| [ZSCORE](zscore/Zscore.md) | Z-Score | Standard deviations from mean. Normalizes different scales. |
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| [ZTEST](ztest/Ztest.md) | Z-Test | One-sample t-test statistic against hypothesized mean. |
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