Key Concepts of Unit Root Tests to Know for Intro to Time Series

Unit root tests are essential for understanding time series data. They help determine if a series is stationary or has a unit root, impacting how we analyze trends and patterns. Key tests include ADF, PP, KPSS, DF-GLS, and Zivot-Andrews.

1. Augmented Dickey-Fuller (ADF) test

   • Tests the null hypothesis that a unit root is present in a univariate time series.
   • Incorporates lagged differences of the dependent variable to account for autocorrelation.
   • Provides critical values for different significance levels to determine the presence of a unit root.
   • Can be adjusted for trends and seasonal components in the data.
   • A rejection of the null hypothesis suggests the series is stationary.

2. Phillips-Perron (PP) test

   • Similar to the ADF test but allows for heteroskedasticity in the error term.
   • Adjusts the test statistics to account for serial correlation without adding lagged terms.
   • Tests the null hypothesis of a unit root in the time series.
   • Provides robust critical values for inference.
   • Useful for series with non-constant variance over time.

3. Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test

   • Tests the null hypothesis that a time series is stationary around a deterministic trend.
   • Complementary to ADF and PP tests, as it focuses on stationarity rather than the presence of a unit root.
   • Can be applied to both level and trend stationary series.
   • Provides critical values for different significance levels to assess stationarity.
   • A rejection of the null hypothesis indicates the presence of a unit root.

4. Dickey-Fuller GLS (DF-GLS) test

   • An enhancement of the ADF test that uses generalized least squares to improve power.
   • Reduces the size of the test by transforming the series before testing for a unit root.
   • More efficient in detecting unit roots in small samples compared to the standard ADF test.
   • Can be applied to both trend and level stationary series.
   • Provides critical values that differ from those of the ADF test.

5. Zivot-Andrews test

   • Tests for a unit root in the presence of a structural break in the time series.
   • Allows for the identification of a single break point, which can significantly affect the series' properties.
   • Tests the null hypothesis of a unit root against the alternative of stationarity with a break.
   • Provides critical values that account for the presence of a break.
   • Useful for analyzing economic and financial time series that may experience sudden shifts.