A Note on Teaching Infinite Moving Averages

Fuller (1976), Anderson (1971), and Hannan (1970) introduce infinite moving average models as the limit in the quadratic mean of a sequence of partial sums, and Fuller (1976) shows that if the assumption of independence of the addends is made then the limit almost surely holds.This note shows that without the assumption of independence, the limit holds with probability one.Moreover, the proofs given here are easier to teach.