Premium
On modelling and diagnostic checking of vector periodic autoregressive time series models
Author(s) -
Ursu Eugen,
Duchesne Pierre
Publication year - 2009
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2008.00601.x
Subject(s) - autocovariance , autoregressive model , mathematics , series (stratigraphy) , residual , asymptotic distribution , estimator , autocorrelation , autoregressive–moving average model , bivariate analysis , statistics , econometrics , algorithm , mathematical analysis , paleontology , fourier transform , biology
. Vector periodic autoregressive time series models (PVAR) form an important class of time series for modelling data derived from climatology, hydrology, economics and electrical engineering, among others. In this article, we derive the asymptotic distributions of the least squares estimators of the model parameters in PVAR models, allowing the parameters in a given season to satisfy linear constraints. Residual autocorrelations from classical vector autoregressive and moving‐average models have been found useful for checking the adequacy of a particular model. In view of this, we obtain the asymptotic distribution of the residual autocovariance matrices in the class of PVAR models, and the asymptotic distribution of the residual autocorrelation matrices is given as a corollary. Portmanteau test statistics designed for diagnosing the adequacy of PVAR models are introduced and we study their asymptotic distributions. The proposed test statistics are illustrated in a small simulation study, and an application with bivariate quarterly West German data is presented.