Hidden regular variation of moving average processes with heavy-tailed innovations

Abstract

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.