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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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Weak stationarity and ARMA-ARCH/GARCH models?
Strict stationarity is the strongest form of stationarity. It means that the joint statistical distribution of any collection of the time series variates never depends on time. … However, for day to day use strict stationarity is too strict. Hence, the following weaker definition is often used instead. …