Fixed-smoothing asymptotics for time series

TL;DR

This paper develops higher order Edgeworth expansions for subsampling-based t-statistics and Wald statistics under fixed-smoothing, demonstrating second-order correctness of a new bootstrap method in Gaussian models.

Contribution

It derives explicit higher order asymptotic expansions and validates the Gaussian dependent bootstrap's accuracy in Gaussian location models.

Findings

Error of asymptotic approximation is of order 1/n

Explicit forms for leading error terms are obtained

Gaussian dependent bootstrap is second-order correct

Abstract

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based t-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model.