Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters
Article first published online: 8 FEB 2009
© 2009 The Authors. Journal compilation © 2009 VVS
Volume 63, Issue 2, pages 183–212, May 2009
How to Cite
Ursu, E. and Duchesne, P. (2009), Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters. Statistica Neerlandica, 63: 183–212. doi: 10.1111/j.1467-9574.2009.00417.x
- Issue published online: 26 MAR 2009
- Article first published online: 8 FEB 2009
- Received: December 2007. Revised: December 2008.
- diagnostic checking;
- periodic time series;
- portmanteau test statistics;
- residual autocorrelation and autocovariance matrices;
- seasonal time series;
- vector time series
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.