Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 218 / 6 / b / Solution

An MA($q$) process is invertible when its innovations admit a causal absolutely summable linear representation in present and past observations. With the backshift operator $B$, MA(1) satisfiesIf $|\theta |<1$, the geometric series converges absolutely:Thus the process is invertible.