Some Thoughts on the Estimation of the Autocorrelation Function

• Activity Number: 601
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Wayne Woodward*+
• Companies: Southern Methodist University
• Keywords: sample autocorrelations ; stationary process ; Burg estimates

Abstract

Estimation of the autocorrelation function is a key step in the analysis of stationary time series data. While Yule-Walker estimates of the parameters of an AR(p) process have given way to more sophisticated methods such as ML and Burg estimation, the autocorrelation function continues to be estimated using the widely used sample autocorrelation function (see Box, Jenkins, and Reinsel (2008) and Woodward, Gray, and Elliott (2012)). In this paper we discuss alternative estimation techniques and focus most attention on a Burg autocorrelation estimator. The properties of autocorrelation estimators are compared and contrasted. Simulation results are given that illustrate the fact that, while Burg and sample autocorrelations are often quite similar, Burg autocorrelation estimates can be substantially better than sample autocorrelations in certain cases.