7. SARIMA and periodic correlation processes

Here we present two classes of processes that are more or less periodic in nature:

• SARIMAs (for Seasonal ARIMAs) exhibit periodic variations that are themselves random in nature. SARIMAs are stationary when they are not integrated (SARMAs), and non-stationary when they are integrated (like ARIMAs);

• Periodically Correlated Random Processes (PCRP) are non-stationary, their covariance γ _X (t ₁ , t ₂ ) being periodic with respect to t ₁ and t ₂ . We'll see that, under certain conditions, such processes can find a stationary pattern if we represent them in multivariate form.

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