Subsampling for heteroskedastic time series

In this article, a general theory for the construction of confidence intervals or regions in the context of heteroskedastic-dependent data is presented. The basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data. This method was first proposed by Politis and Romano (1994b) for stationary observations. We extend their results to heteroskedastic observations, and prove a general asymptotic validity result under minimal conditions. In contrast, the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case-by-case analysis. Our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors.