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Miha Kralj
2026-03-16 12:46:19 -07:00
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lib/statistics/adf/Adf.md
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| **PineScript** | [adf.pine](adf.pine) |
- Tests the null hypothesis that a time series contains a unit root (non-stationary). Output near **0** → stationary; output near **1** → unit root.
- **Similar:** [Hurst](../hurst/Hurst.md), [Cointegration](../cointegration/Cointegration.md) | **Complementary:** Z-Score, Variance | **Trading note:** ADF < 0.05 confirms mean-reversion suitability.
- **Similar indicators:** [Hurst](../hurst/Hurst.md), [Cointegration](../cointegration/Cointegration.md)
- **Complementary indicators:** [Z-Score](../zscore/Zscore.md), [Variance](../variance/Variance.md)
- **Trading note:** ADF < 0.05 confirms mean-reversion suitability.
- Validated against Python `statsmodels.tsa.stattools.adfuller` reference implementation.
The Augmented Dickey-Fuller test is the gold standard for detecting whether a financial time series is stationary or contains a unit root. Unlike the original Dickey-Fuller test, the augmented version includes lagged difference terms $\Delta y_{t-i}$ to absorb serial correlation, ensuring the test statistic follows the correct distribution. The p-value output uses MacKinnon (1994, 2010) polynomial interpolation with a standard normal CDF approximation, providing machine-precision results without lookup tables.