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Adaptive inference of autoregressive models under nonnormality

Yentür, Begüm
Recently, non-normal innovations in autoregressive models have become prevalent in many applications. In this case, it is known that the least squares (LS) estimators are neither efficient nor robust. Also, obtaining maximum likelihood (ML) estimators requires numerical solution which is a formidable task. To overcome these difficulties modified maximum likelihood (MML) estimation technique is used to obtain the estimators of the model parameters. In this method, although explicit solution can be found, the necessity of knowing the shape parameter becomes a drawback especially in machine data processing. That is why, in this thesis adaptive modified maximum likelihood (AMML) methodology which combines MML estimation technique with Huber’s M-estimation procedure is used so that the shape parameter can also be estimated. Expectation Maximization (EM) algorithm is also used in order to obtain Maximum Likelihood Estimators (MLEs) numerically. Then, through a simulation study, efficiency and robustness properties of the estimators are discussed and compared with each other. Finally, test statistics are proposed for the crucial parameters of the model. The power comparisons of the test statistics under each estimation technique are presented.