İstatistik Bilim Dalı Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/4382

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Adaptive Estimation of Autoregressive Models Under Long-Tailed Symmetric Distribution
(Association for Computing Machinery, 2019) Yentür, B.; Bayrak, Ö.T.; Akkaya, A.D.
In this paper, we consider the autoregressive models where the error term is non-normal; specifically belongs to a long-tailed symmetric distribution family since it is more relevant in practice than the normal distribution. It is known that least squares (LS) estimators are neither efficient nor robust under non-normality and maximum likelihood (ML) estimators cannot be obtained explicitly and require a numerical solution which might be problematic. In recent years, modified maximum likelihood (MML) estimation is developed to overcome these difficulties. However, this method requires that the shape parameter is known which is not realistic in machine data processing. Therefore, we use adaptive modified maximum likelihood (AMML) technique which combines MML with Huber’s estimation procedure so that the shape parameter is also estimated. After derivation of the AMML estimators, their efficiency and robustness properties are discussed through a simulation study and compared with MML and LS estimators. © 2019 Association for Computing Machinery.
Citation - Scopus: 1
Inference of Autoregressive Model With Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions
(Springer international Publishing Ag, 2018) Bayrak, Ozlem Tuker; Akkaya, Aysen Dener
In classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the authors. In this situation, maximum likelihood estimation technique is problematic and requires numerical solution which may have convergence problems and can cause bias. Besides, statistical properties of the estimators can not be obtained due to non-explicit functions. It is also known that least squares estimation technique yields neither efficient nor robust estimators. Therefore, modified maximum likelihood estimation technique is utilized in this study. It is shown that the estimators are highly efficient, robust to plausible alternatives having different forms of symmetric short-tailedness in the sample and explicit functions of data overcoming the necessity of numerical solution. A real life application is also given.

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