A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations

Abstract

In this article we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes part in the space of c\`{a}dl\`{a}g functions on $[0,1]$ with the Skorokhod $M_{2}$ topology.