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 $({\psi }_j:j\ge 0)$. Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.

13 pages