Bootstrap estimation of sample autocorrelation functions

Abstract

It is rarely appreciated that the sample autocorrelation function is a non-stationary stochastic process with mean and variance that are functions of the lag distance. For Gaussian processes, some complex formulae for the mean and covariance of the sample autocorrelation function are available. Analytical solutions for non-Gaussian processes are probably intractable and none seems to be available. A more hopeful strategy is to exploit growing desktop computational power and increasingly powerful simulation techniques for stochastic processes to perform bootstrapping. Numerical results presented in this study show that fairly accurate mean estimates of the sample autocorrelation function can be obtained for both Gaussian and non-Gaussian processes using bootstrapping. Variance estimates are less accurate, but even crude estimates are useful in identifying the level of noise at large lags and reducing misinterpretation of how the actual autocorrelation function decays with lag distance. Copyright ASCE 2006.