Subsampling for Heteroscedastic Time Series

In this article, a general theory for the construction of confidence intervals or regions in the context of heteroskedastic depended data is presented. The basic idea is to approximate the sampling distributaion of a statisctic 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 ovservations. We extend their results to heteroskedastic observations, and prove a general asymptotic validity result under minimal conditions. In contrast the usual bootstrap and moveing blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis. Our general asymptotic results are aplied to a regression setting with dependent heteroskedastic errors