We look at joint regular variation properties of MA($\infty$) processes of the form $\mathbf{ X} = (X_k, k \in \mathbb{ Z})$ where $X_k = \sum_{ j=0}^{ \infty} \psi_j Z_{ k-j}$ and the sequence of random variables $(Z_i, i \in \mathbb{ Z})$ are i.i.d. with regularly varying tails. We use the setup of $\mathbb{ M}_{ \mathbb{ O}}$-convergence and obtain hidden regular variation properties for $\mathbf{ X}$ under suitable summability conditions on the constant coefficients $(\psi_j : j \geq 0)$. Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.
Categories: math.PR