Two New Estimators for the Autocorrelation Function Through Singular Spectrum Analysis

Abstract

It is around a century that sample autocorrelation function has been introduced and used as a standard tool in time series analysis. A vast literature can be found on the statistical properties of the sample autocorrelation function. However, it has been highlighted recently that the sum of the sample autocorrelation function over the lags 1 to $T-1$ is −0.5 for all time series of length T. This property produces a big concern for the cases in which all available sample autocorrelations are used in the inference.

This paper provides two new alternative for estimating the autocorrelation function. These estimators come from the idea of singular spectrum analysis which is a non-parametric technique for time series analysis. The paper utilizes a simulation study to illustrate the performance of the new approach. The results suggest that further improvement to the sample autocorrelation is possible and the new methods provide an attractive alternative to the classical approach.