Asymptotic Distributions of the Sample Mean, Autocovariances and Autocorrelations of Long-Memory Time Series.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Persistence, or long memory, is the presence in a time series of significant dependence between observations a long time span apart. Correct identification of long memory in an observed time series can greatly improve the accuracy of long-range forecasts of the series, and can give a better understanding of the physical processes which generate the observed series. The long-memory phenomenon has been observed by researchers in a number of areas of application including economics, geophysics, hydrology and meteorology. This report derives the distributions of the sample autocorrelations and related quantities when the samples size is large, thereby facilitating the diagnosis of long memory in an observed time series.
- Statistics and Probability