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Estimating multivariate autoregressive moving average models by fitting long autoregressions
Authors:Pentti Saikkonen  Ritva Luukkonen
Institution:1. Department of Statistics , University of Helsinki , Aleksanterinkatu 7, Helsinki, 00100, Finland;2. Institute of Occupational Health , Topeliuksenkatu 41 a A, Helsinki, 00250, Finland
Abstract:Some simple methods for the estimation of mixed multivariate autoregressive moving average time series models are introduced. The methods require the fitting of a long autoregression to the data and the computation of consistent initial estimates for the parameters of the model. After these preliminaries the estimators of the paper are obtained by applying weighted least squares to a multivariate auxiliary regression model. Two types of weight matrices are considered. Both of them yield estimators which are strongly consistent and asymptotically normally distributed. The first estimators are also asymptotically efficient while the second ones are not fully efficient but computationally simple. A simulation study is performed to illustrate the behaviour of the estimators in finite samples.
Keywords:asymptotic efficiency  asymptotic normality  long autoregression  multivariate autoregressive moving average model  strong consistency
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