2 Moving average models Definition. The moving average model of order q, or MA(q), is defined to be Xt = t + θ1 t−1 + θ2 t−2 + · · ·+ θq t−q, where t i.i.d. ∼ N(0, σ). Remarks: 1. Without loss of generality, we assume the mean of the process to be zero. 2. Here θ1, . . . , θq (θq 6= 0) are the parameters of the model. 3. Sometimes it suffices to assume that t ∼WN(0, σ). Here we assume normality...

We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localisable and we characterize the nature of the associated tangent processes. Examples include t...