Glossary
Stationarity
A time series is stationary if its mean, variance, and autocovariance structure do not change over time. Stationarity is a critical assumption in most time-series models. When a series is non-stationary due to a unit root, differencing typically restores stationarity.
Definition
A time series is stationary if its mean, variance, and autocovariance structure do not change over time. Stationarity is a critical assumption in most time-series models. When a series is non-stationary due to a unit root, differencing typically restores stationarity.
Why It Matters
Most time-series models, including ARMA and VAR, assume stationarity. Violating this assumption leads to spurious regressions, inconsistent estimators, and misleading inference. Determining whether a series is stationary, trend-stationary, or difference-stationary is the essential first step in any time-series analysis, because it dictates whether to model in levels, detrended data, or differences.
Example
The Turkish CPI index is clearly non-stationary: its mean drifts upward over decades, and its variance grows with the price level. A unit-root test confirms the presence of a unit root. After first-differencing, the inflation series (CPI growth rate) is stationary with a roughly constant mean and variance, making it suitable for ARMA modelling and VAR analysis.
Related Terms
Software Notes
- SPSS: Use Analyze > Forecasting > Time Series Modeling for basic stationarity diagnostics. For formal unit-root tests, use R integration.
- R: Use
adf.test()fromtseriesorur.df()fromurcafor ADF tests, andkpss.test()fromtseriesfor the KPSS test (which has stationarity as the null hypothesis). - Stata: Use
dfullerfor the ADF test andkpssfor the KPSS test. Always complement ADF (null: unit root) with KPSS (null: stationarity) for robust conclusions.
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