UnitRootTests

UnitRootTests are statistical procedures used in time series analysis to determine whether a series is non-stationary due to a unit root. A unit root implies that shocks have permanent effects and that the series follows a stochastic trend, which can affect forecasting and model specification. When a unit root is present, differencing the data once or more often renders it stationary, a common step in ARIMA modeling. These tests guide the choice of differencing and inform subsequent tests of cointegration in multivariate settings.

Common tests include the Augmented Dickey-Fuller (ADF) test, which assesses the null hypothesis of a unit root against stationarity, typically with options for no, or with an intercept and/or a deterministic trend. The Dickey-Fuller test is a simpler version used when fewer lags are appropriate. Phillips-Perron (PP) tests adjust for serial correlation and heteroskedasticity without adding lagged differenced terms. The DF-GLS test improves power by pre-detrending the series with a generalized least squares approach. The KPSS test, in contrast, tests the null of stationarity (no unit root) and is often used alongside unit root tests to triangulate conclusions.

Interpretation hinges on the test specification, including deterministic terms and lag selection. Null hypotheses, power, and size distortions can be sensitive to sample size, structural breaks, and nonlinearity. In practice, researchers compare several tests and consider the economic or scientific context before deciding on differencing or model form. Software implementations are widespread, including R packages for ADF and PP tests, Python libraries in statsmodels, and econometrics suites in EViews or Stata.

See also: stationarity, cointegration, ARIMA.