Bootstrap estimates of the sample bivariate autocorrelation and partial autocorrelation distributions

Abstract

This paper shows how the bootstrap method can be used to estimate the joint distribution of sample autocorrelations and partial autocorrelations. The exact joint distribution of sample autocorrelations is mathematically intractable and attempts at workable approximations are difficult and rely on special assumptions. The bootstrap offers an accurate solution to this problem without requiring special assumptions and in a way that avoids theoretical difficulties. The bootstrap-estimated joint distributions of the autocorrelations and partial autocorrelations of time series are shown to lead to better ARMA model identification. This is demonstrated using simulated series.

Keywords:

• Time series
• Autoregressive models
• Bootstrap statistics
• Autocorrelation functions
• Partial autocorrelation functions