Subsampling inference for the autocorrelations of GARCH processes

We provide self-normalization for the sample autocorrelations of power GARCH(p,q) processes whose higher moments might be infinite. To validate the studentization, whose goal is to match the growth rate dependent on the index of regular variation of the process, we substantially extend existing weak-convergence results.
Since asymptotic distributions are non-pivotal, we construct subsampling-based
confidence intervals for the autocorrelations and cross-correlations, which are shown to have satisfactory empirical coverage rates in a simulation study. The methodology is further applied to daily returns of CAC40 and FTSA100 indices and their squares.