Derivation of the Variance for a Stationary AR(1) Process

Students frequently overlook the critical stationarity condition

|\phi| < 1

, which permits the assumption

Var(X_t) = Var(X_{t-1})

. They might also forget that the covariance

Cov(X_{t-1}, \epsilon_t) = 0

is a crucial assumption, or that the constant

c

vanishes during variance calculation.

Institutional Reference: Time Series Analysis