Multivariate portmanteau tests for weak multiplicative seasonal VARMA models

Abdoulkarim Ilmi Amir () and Yacouba Boubacar Maïnassara ()
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Abdoulkarim Ilmi Amir: Université Bourgogne Franche-Comté, UMR CNRS 6623
Yacouba Boubacar Maïnassara: Université Bourgogne Franche-Comté, UMR CNRS 6623

Statistical Papers, 2020, vol. 61, issue 6, No 12, 2529-2560

Abstract: Abstract Numerous multivariate time series encountered in real applications display seasonal behavior. In this paper we consider portmanteau tests for testing the adequacy of structural multiplicative seasonal vector autoregressive moving-average (SVARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak SVARMA). We study the asymptotic distributions of residual autocorrelations at seasonal lags of multiple of the length of the seasonal period under weak assumptions on the noise. We deduce the asymptotic distribution of the proposed multivariate portmanteau statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. A set of Monte Carlo experiments and an application of U.S. monthly housing starts and housing sold are presented.

Keywords: Goodness-of-fit test; Quasi-maximum likelihood estimation; Portmanteau tests; Residual autocorrelation; Weak SVARMA models; Primary 62M10; 62F03; 62F05; Secondary 91B84; 62P05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-018-1055-4

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