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Intermediate Proof

Derivation of the Autocorrelation Function (ACF) for an MA(q) Process, demonstrating its Cut-off Property

Students frequently confuse the cut-off property of the ACF for MA(q) processes with the cut-off property of the Partial Autocorrelation Function (PACF) for AR(p) processes. They also often struggle with the precise summation limits and the conditions for non-zero expectations when calculating autocovariances, especially identifying when ϵtjϵtkl \epsilon_{t-j}\epsilon_{t-k-l} terms are non-zero.
Institutional Reference: Time Series Analysis
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