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...
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.
Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models
Yozgatlıgil, Ceylan (Informa UK Limited, 2009-11-01)
Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this articl...
Polynomial solutions of the Schrodinger equation for the generalized Woods-Saxon potential
Berkdemir, C; Berkdemir, A; Sever, Ramazan (American Physical Society (APS), 2005-08-01)
The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential are obtained by means of Nikiforov-Uvarov (NU) method. Certain bound states of the Schrodinger equation for the potential are calculated analytically and the wave functions are found in terms of the Jacobi polynomials. It is shown that the results are in good agreement with those obtained previously.
Multisymplectic Schemes for the Complex Modified Korteweg-de Vries Equation
AYDIN, AYHAN; Karasözen, Bülent (2008-09-20)
In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
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: