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Medium · Machine Learning & Time Series · Numerical · ~5 min · #37

Stationary Variance of an AR(1)

Consider the stationary AR(1) process

Xt=0.8 Xt−1+εt,εt∼iid(0,1).X_t = 0.8\,X_{t-1} + \varepsilon_t, \qquad \varepsilon_t \overset{\text{iid}}{\sim} (0, 1).

What is Var⁡(Xt)\operatorname{Var}(X_t)?

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StationarityAR(1) variancePersistence

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