ADF Test

Augmented Dickey-Fuller (ADF) Test

The ADF test is a statistical procedure used to determine whether a time series is stationary or non-stationary. It is an extension of the Dickey-Fuller test that allows testing for stationarity in series with more complex autocorrelation structures by including multiple lags.

Hypotheses

1. Null hypothesis ($H_0$): The series is non-stationary (has a unit root).
2. Alternative hypothesis ($H_A$): The series is stationary (no unit root).

Key Concepts

• Unit root: Indicates that (Time Series Shocks) shocks to the time series have a permanent effect and the series is non-stationary.
• Integration:
  • If differencing a non-stationary series once produces a stationary series, it is said to be integrated of order 1 ($I(1)$).
  • Some processes may require differencing multiple times (order $d>1$).
• Mean reversion (Mean reverting): A stationary series tends to revert around a constant mean (can be sinusoidal).

Notes

• The ADF test generalizes the Dickey-Fuller test by testing multiple lags simultaneously.
• Its conclusion focuses on the absence of a unit root, indicating stationarity.
• Useful reference: Dickey-Fuller Test.