The sample autocorrelation function and the detection of long-memory processes

Hassani, Hossein, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Patterson, K. 2012. The sample autocorrelation function and the detection of long-memory processes. Physica A: Statistical Mechanics and its Applications 391 (24) , pp. 6367-6379. 10.1016/j.physa.2012.07.062

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Abstract

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Long-range dependence; Long-memory process; Sample autocorrelation function; Spectral density function; Auto bicorrelations; Bispectral density
Publisher:	Elsevier
ISSN:	0378-4371
Last Modified:	24 Oct 2022 10:38
URI:	https://orca.cardiff.ac.uk/id/eprint/45217

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