Bootstrapping non-stationary and irregular time series using singular spectral analysis

Abstract

This article investigates the consequences of using Singular Spectral Analysis (SSA) to construct a time series bootstrap. The bootstrap replications are obtained via a SSA decomposition obtained using rescaled trajectories (RT-SSA), a procedure that is particularly useful in the analysis of time series that exhibit nonlinear, non-stationary and intermittent or transient behaviour. The theoretical validity of the RT-SSA bootstrap when used to approximate the sampling properties of a general class of statistics is established under regularity conditions that encompass a very broad range of data generating processes. A smeared and a boosted version of the RT-SSA bootstrap are also presented. Practical implementation of the bootstrap is considered and the results are illustrated using stationary, non-stationary and irregular time series examples.