Subsampling inference for the autocovariances and autocorrelations of long-memory time series
We provide a self-normalization for the sample acvs and acs of a linear, long-memory time series with innovations that have either finite 4th moment or are heavy-tailed with tail index $2<\alpha<4$. In the asymptotic distribution of the sample acv there are three rates of convergence that depend on the interplay between the memory parameter d and alpha, and which consequently lead to three different limit distributions; for the sample ac the limit distribution only depends on d. We introduce a self-normalized sample acv statistic, which is computable without knowledge of alpha or d, and which converges to a nondegenerate distribution. We also treat self-normalization of the acs. The sampling distributions can then be approximated nonparametrically by subsampling, as the asymptotic distribution is still parameter-dependent. The subsampling-based confidence intervals for the process acvs and acs are shown to have satisfactory empirical coverage rates in a simulation study.
Palabras clave: linear time series parameter-dependent convergence rates self-normalization subsampling confidence intervals
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