Bayesian Subset Selection of Seasonal Autoregressive Models
Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these mod...
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2878 |
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| author | Ayman A. Amin Walid Emam Yusra Tashkandy Christophe Chesneau |
| author_facet | Ayman A. Amin Walid Emam Yusra Tashkandy Christophe Chesneau |
| author_sort | Ayman A. Amin |
| collection | DOAJ |
| description | Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm. |
| first_indexed | 2024-03-11T01:35:28Z |
| format | Article |
| id | doaj.art-b0018778c92e4a5691ad914d78783f5f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:28Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b0018778c92e4a5691ad914d78783f5f2023-11-18T17:02:38ZengMDPI AGMathematics2227-73902023-06-011113287810.3390/math11132878Bayesian Subset Selection of Seasonal Autoregressive ModelsAyman A. Amin0Walid Emam1Yusra Tashkandy2Christophe Chesneau3Department of Statistics, Mathematics, and Insurance, Faculty of Commerce, Menoufia University, Menoufia 32952, EgyptDepartment of Statistics and Operation Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operation Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, University of Caen-Normandie, 14000 Caen, FranceSeasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm.https://www.mdpi.com/2227-7390/11/13/2878SAR modelsSSVS procedureposterior analysismixture–normal |
| spellingShingle | Ayman A. Amin Walid Emam Yusra Tashkandy Christophe Chesneau Bayesian Subset Selection of Seasonal Autoregressive Models Mathematics SAR models SSVS procedure posterior analysis mixture–normal |
| title | Bayesian Subset Selection of Seasonal Autoregressive Models |
| title_full | Bayesian Subset Selection of Seasonal Autoregressive Models |
| title_fullStr | Bayesian Subset Selection of Seasonal Autoregressive Models |
| title_full_unstemmed | Bayesian Subset Selection of Seasonal Autoregressive Models |
| title_short | Bayesian Subset Selection of Seasonal Autoregressive Models |
| title_sort | bayesian subset selection of seasonal autoregressive models |
| topic | SAR models SSVS procedure posterior analysis mixture–normal |
| url | https://www.mdpi.com/2227-7390/11/13/2878 |
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