A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology

Abstract

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of real-valued cadlag functions on $[0,1]$ with the Skorokhod $M_{1}$ topology.