Testing for stationarity in time series

A stationary time series is a series in which statistical properties such as mean, variance, and covariance are constant over time. Stationarity is a desired characteristic of time series as it makes modeling and extrapolating (forecasting) into the future more feasible. Some drawbacks of non-stationary data are:

• Variance can be misspecified by the model
• Worse model fit
• Cannot leverage valuable time-dependent patterns in the data

In this recipe, we show you how to test the time series for stationarity. To do so, we employ the following methods:

• The Augmented Dickey-Fuller (ADF) test
• The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test
• Plots of the (partial) autocorrelation function (PACF/ACF)

We investigate the stationarity of monthly gold prices from the years 2000-2011.

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