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A strictly stationary process (or time series) is one whose joint distribution is constant over time shifts. A weakly stationary (or covariance stationary) process or series is one whose mean and covariance function (variance and autocorrelation function) do not change over time.
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Stationarity of AR(1) process whose autoregressive parameter could change over time
Imagine an AR(1) has an autoregressive parameter which could change in time.
$y_t-\mu=\phi_t (y_{t-1}-\mu)+\varepsilon_t\,$, where $\phi_t$ is not always constant but still lies inside the usual bou …