Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions

Bayrak, Ozlem Tuker
Akkaya, Ayşen
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.


Nonnormal regression. I. Skew distributions
İslam, Muhammed Qamarul; Yildirim, F (2001-01-01)
In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we deriv...
Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations
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The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] who give solutions for a simple AR(I) model
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Guven, Bilgehan; Kotz, Samual (2008-01-15)
Given a pair of absolutely continuous random variables (X, Y) distributed as the generalized Farlie-Gumbel-Morgenstern (GFGM) distribution, we develop a test for testing the hypothesis: X and Y are independent vs. the alternative; X and Y are positively (negatively) quadrant dependent above a preassigned degree of dependence. The proposed test maximizes the minimum power over the alternative hypothesis. Also it possesses a monotone increasing power with respect to the dependence parameter of the GFGM distri...
Binary regression with stochastic covariates
Oral, E. (2006-01-01)
In binary regression the risk factor X has been treated in the literature as a non-stochastic variable. In most situations, however, X is stochastic. We present solutions applicable to such situations. We show that our solutions are more precise than those obtained by treating X as non-stochastic when, in fact, it is stochastic.
Hypothesis testing in one-way classification AR(1) model with Student’s t innovations: An application to a real life data
Yıldırım, Özgecan; Yozgatlıgil, Ceylan; Şenoğlu, Birdal (null; 2017-05-26)
In this study, we estimate the model parameters in one-way classification AR (1) model when the distribution of the error terms is independently and identically distributed (iid) Student’s t. Maximum likelihood (ML) methodology is used in the estimation procedure. We also introduce the F statistic based on the ML estimators of the parameters for testing the equality of the treatment means. See also Yıldırım (2017) (M.S. Thesis, METU, Ankara, Continue) and Şenoğlu and Bayrak (2016) (Linear Contrasts in one-w...
Citation Formats
O. T. Bayrak and A. Akkaya, “Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, pp. 2105–2116, 2018, Accessed: 00, 2020. [Online]. Available: