Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the p... more Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the parameters to vary with seasons. Selecting PAR time-series models can be computationally expensive, and the results are not always satisfactory. In this article, we propose a new automatic procedure to the model selection problem by using the genetic algorithm. The Bayesian information criterion is used as a tool to identify the order of the PAR model. The success of the proposed procedure is illustrated in a small simulation study, and an application with monthly data is presented.
We introduce a class of multivariate seasonal time series models with periodically varying parame... more 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.
Abstract. Vector periodic autoregressive time series models (PVAR) form an important class of ti... more Abstract. 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.
Many time series encountered in real applications display seasonal behavior. In this paper, we co... more Many time series encountered in real applications display seasonal behavior. In this paper, we consider multiplicative seasonal vectorial autoregressive moving average (SVARMA) models to describe seasonal vector time series. We discuss conditional maximum likelihood estimation of the model parameters, allowing them to satisfy general linear constraints. Having fitted a model, residual autocovariances (or autocorrelations) have been found useful in checking time series models. Consequently, we obtain the asymptotic distributions of the residual autocovariance matrices. As applications of these results, Portmanteau test statistics are proposed and their asymptotic distributions are studied. The finite-sample properties of the test statistics are evaluated using Monte Carlo experiments.
Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the p... more Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the parameters to vary with seasons. Selecting PAR time-series models can be computationally expensive, and the results are not always satisfactory. In this article, we propose a new automatic procedure to the model selection problem by using the genetic algorithm. The Bayesian information criterion is used as a tool to identify the order of the PAR model. The success of the proposed procedure is illustrated in a small simulation study, and an application with monthly data is presented.
We introduce a class of multivariate seasonal time series models with periodically varying parame... more 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.
Abstract. Vector periodic autoregressive time series models (PVAR) form an important class of ti... more Abstract. 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.
Many time series encountered in real applications display seasonal behavior. In this paper, we co... more Many time series encountered in real applications display seasonal behavior. In this paper, we consider multiplicative seasonal vectorial autoregressive moving average (SVARMA) models to describe seasonal vector time series. We discuss conditional maximum likelihood estimation of the model parameters, allowing them to satisfy general linear constraints. Having fitted a model, residual autocovariances (or autocorrelations) have been found useful in checking time series models. Consequently, we obtain the asymptotic distributions of the residual autocovariance matrices. As applications of these results, Portmanteau test statistics are proposed and their asymptotic distributions are studied. The finite-sample properties of the test statistics are evaluated using Monte Carlo experiments.
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Papers by Eugen Ursu