Resampling time series by missing values techniques

Abstract

For strongly dependent data, deleting blocks of observations is expected to produce bias as in the moving block jackknife of KOnsch (1989) and Liu and Singh (1992). We propose an alternative technique which considers the blocks of deleted observations in the blockwise jackknife as missing data which are replaced by missing values estimates incorporating the observations dependence structure. Thus, the variance estimator is a weighted sample variance of the statistic evaluated in a "complete" series. We establish consistency for the variance and distribution of the sample mean. Also we extent this missing values approach to the blockwise bootstrap by assuming some missing observations among two consecutive blocks. We present the results of an extensive Monte Carlo study to evaluate the performance of the proposed methods in finite sample sizes in which it is shown that our proposal produces estimates of the variance of several time series statistics with smaller mean squared error than previous procedures.