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Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Eugen Ursu, Pierre Duchesne

Editorial: Statistica Neerlandica, 63 (2), p.183-212, 2009.


We introduce a class of multivariate seasonal time series models with periodically varying parameters, abbreviated by the acronym SPVAR. The model is suitable for multivariate data, and combines a periodic autoregressive structure and a multiplicative seasonal time
series model. The stationarity conditions (in the periodic sense) and
the theoretical autocovariance functions of SPVAR stochastic processes
are derived. Estimation and checking stages are considered. The asymptotic normal distribution of the least squares estimators of the model parameters is established, and the asymptotic distributions of the residual autocovariance and autocorrelation matrices in the class of SPVAR time series models are obtained. In order to check model adequacy, portmanteau test statistics are considered and their asymptotic distributions are studied. A simulation study is briefly discussed
to investigate the finite-sample properties of the proposed test
statistics.The methodology is illustrated with a bivariate quarterly data set on travelers entering in to Canada.

Cuvinte cheie: diagnostic checking, periodic time series, portmanteau test statistics, residual autocorrelation and autocovariance matrices, seasonal time series, vector time series // statistics, time series