Moment Tests for Window Length Selection in Singular Spectrum Analysis of Short- and Long-Memory Processes

Atikur Khan and Donald Poskitt

No 22/11, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: In this paper we propose a new methodology for selecting the window length in Singular Spectral Analysis in which the window length is determined from the data prior to the commencement of modeling. The selection procedure is based on statistical tests designed to test the convergence of the autocovariance function. A classical time series portmanteau type statistic and two test statistics derived using a conditional moment principle are considered. The first two are applicable to short-memory processes, and the third is applicable to both short- and long-memory processes. We derive the asymptotic distribution of the statistics under fairly general regularity conditions and show that the criteria will identify true convergence with a finite window length with probability one as the sample size increases. Results obtained using Monte-Carlo simulation indicate the relevance of the asymptotic theory, even in relatively small samples, and that the conditional moment tests will choose a window length consistent with the Whitney embedding theorem. Application to observations on the Southern Oscillation Index shows how observed experimental behaviour can be reflected in features seen with real world data sets.

Keywords: Portmanteau type test; Conditional moment test; Asymptotic distribution; Linear regular process; Singular spectrum analysis; Embedding (search for similar items in EconPapers)
JEL-codes: C12 C22 C52 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2011-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Journal Article: Moment tests for window length selection in singular spectrum analysis of short– and long–memory processes (2013)
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