Computation of the autocovariances for time series with multiple long-range persistencies

Tucker McElroy () and Scott H. Holan

Computational Statistics & Data Analysis, 2016, vol. 101, issue C, 44-56

Abstract: Gegenbauer processes allow for flexible and convenient modeling of time series data with multiple spectral peaks, where the qualitative description of these peaks is via the concept of cyclical long-range dependence. The Gegenbauer class is extensive, including ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Model estimation is challenging for Gegenbauer processes when multiple zeros and poles occur in the spectral density, because the autocovariance function is laborious to compute. The method of splitting–essentially computing autocovariances by convolving long memory and short memory dynamics–is only tractable when a single long memory pole exists. An additive decomposition of the spectrum into a sum of spectra is proposed, where each summand has a single singularity, so that a computationally efficient splitting method can be applied to each term and then aggregated. This approach differs from handling all the poles in the spectral density at once, via an analysis of truncation error. The proposed technique allows for fast estimation of time series with multiple long-range dependences, which is illustrated numerically and through several case-studies.

Keywords: Gegenbauer; Long memory; Long-range dependence; Quasi-biennial oscillations; Seasonal long memory; Spectral density (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947316300202
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:101:y:2016:i:c:p:44-56

DOI: 10.1016/j.csda.2016.02.004

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().