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Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions
Date
2018-12-01
Author
Bayrak, Ozlem Tuker
Akkaya, Ayşen
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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.
Subject Keywords
Autoregression
,
Modified maximum likelihood
,
Non-normality
,
Robustness
URI
https://hdl.handle.net/11511/46425
Journal
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
DOI
https://doi.org/10.1007/s40995-017-0448-x
Collections
Department of Statistics, Article
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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: https://hdl.handle.net/11511/46425.