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.