Glossary

Unit Root

A characteristic of a time series whose autoregressive polynomial has a root equal to one, implying that shocks have a permanent effect and the series is non-stationary. Testing for unit roots is typically the first step in time-series analysis.

Definition

Why It Matters

The presence of a unit root fundamentally changes how a time series should be modelled and interpreted. A unit-root process wanders without reverting to a fixed mean, making standard regression inference invalid and producing spurious correlations when paired with other trending series. Identifying whether a series contains a unit root determines whether to model it in levels (if stationary), differences (if unit-root non-stationary), or as part of a cointegrated system (if multiple series share a common stochastic trend).

Example

The Turkish nominal GDP series exhibits a clear upward trend and a unit-root test (ADF statistic = -1.2, critical value at 5% = -2.86) fails to reject the null of a unit root. First-differencing yields GDP growth, which passes the stationarity test (ADF statistic = -4.7), confirming that the original series is I(1) and should enter subsequent models in differences or within a cointegration framework.

Related Terms

Software Notes

SPSS: Not directly available; use R integration for unit-root testing.
R: Use adf.test() from tseries for the ADF test, ur.df() from urca for more detailed ADF output, and PP.test() or ur.pp() for the Phillips-Perron test.
Stata: Use dfuller for the ADF test and pperron for the Phillips-Perron test. Both support trend and constant specifications. Use dfgls for the DF-GLS test, which has superior power in small samples.