Explain why a time series needs to be covariance stationary and what it means when a series lacks stationarity
The idea
A series is covariance stationary when its expected value, its variance and its covariance with its own past values are constant and finite over time. Autoregressive models give valid estimates and tests only on stationary series. A series with a trend in its mean, a variance that changes over time, or a unit root is not stationary, and regressions on it can produce impressive but meaningless t-statistics and R². A stationary series has a mean-reverting level it tends back towards, while a non-stationary one does not. The usual fix is to transform it, typically by first-differencing or taking log differences, before modelling. Asset prices and index levels are rarely stationary.
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