Dependence in Probability and Statistics pp 417-426 | Cite as

# Limit Theory for the Sample Correlation Function of Moving Averages

## Abstract

The sample autocorrelation function (acf) is an important statistic in time series analysis. It is frequently relied upon for assessing the dependence structure of a time series and may also be used for model identification and parameter estimation in the class of ARMA models. In this paper, we review some of the main asymptotic results for sample acfs of infinite order moving averages. While the classical theory concerning sample acfs requires the process to have at least finite second moments, our main interest in this paper will be the case when the process has an infinite variance. It turns out that in the infinite variance case, the sample acf can have desirable large sample properties and these can be helpful in estimating various parameters associated with the model.

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