Shrinkage Estimation of Linear Regression Models with GARCH Errors
This paper introduces shrinkage estimators for the parameter vector of a linear regression model with con- ditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2016-11-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25867323.pdf |
| _version_ | 1818534046303518720 |
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| author | S. Hossain M. Ghahramani |
| author_facet | S. Hossain M. Ghahramani |
| author_sort | S. Hossain |
| collection | DOAJ |
| description | This paper introduces shrinkage estimators for the parameter vector of a linear regression model with con- ditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace. We derive the asymp- totic distributional biases and risks of the shrinkage estimators using a large sample theory. We show that if the shrinkage dimension exceeds two, the relative efficiency of the shrinkage estimator is strictly greater than that of the full model estimator. Furthermore, a Monte Carlo simulation study is conducted to examine the relative performance of the shrinkage estimators with the full model estimator. Our large sample theory and simulation study show that the shrinkage estimators dominate the full model estimator in the entire parameter space. We illustrate the proposed method using a real data set from econometrics. |
| first_indexed | 2024-12-11T18:06:39Z |
| format | Article |
| id | doaj.art-a1b7d297f36e4642acd98d76071f11da |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-12-11T18:06:39Z |
| publishDate | 2016-11-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-a1b7d297f36e4642acd98d76071f11da2022-12-22T00:55:43ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872016-11-0115410.2991/jsta.2016.15.4.8Shrinkage Estimation of Linear Regression Models with GARCH ErrorsS. HossainM. GhahramaniThis paper introduces shrinkage estimators for the parameter vector of a linear regression model with con- ditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace. We derive the asymp- totic distributional biases and risks of the shrinkage estimators using a large sample theory. We show that if the shrinkage dimension exceeds two, the relative efficiency of the shrinkage estimator is strictly greater than that of the full model estimator. Furthermore, a Monte Carlo simulation study is conducted to examine the relative performance of the shrinkage estimators with the full model estimator. Our large sample theory and simulation study show that the shrinkage estimators dominate the full model estimator in the entire parameter space. We illustrate the proposed method using a real data set from econometrics.https://www.atlantis-press.com/article/25867323.pdfStein-type shrinkage; likelihood ratio test; linear regression model; GARCH error; asymptotic bias; asymptotic risk. |
| spellingShingle | S. Hossain M. Ghahramani Shrinkage Estimation of Linear Regression Models with GARCH Errors Journal of Statistical Theory and Applications (JSTA) Stein-type shrinkage; likelihood ratio test; linear regression model; GARCH error; asymptotic bias; asymptotic risk. |
| title | Shrinkage Estimation of Linear Regression Models with GARCH Errors |
| title_full | Shrinkage Estimation of Linear Regression Models with GARCH Errors |
| title_fullStr | Shrinkage Estimation of Linear Regression Models with GARCH Errors |
| title_full_unstemmed | Shrinkage Estimation of Linear Regression Models with GARCH Errors |
| title_short | Shrinkage Estimation of Linear Regression Models with GARCH Errors |
| title_sort | shrinkage estimation of linear regression models with garch errors |
| topic | Stein-type shrinkage; likelihood ratio test; linear regression model; GARCH error; asymptotic bias; asymptotic risk. |
| url | https://www.atlantis-press.com/article/25867323.pdf |
| work_keys_str_mv | AT shossain shrinkageestimationoflinearregressionmodelswithgarcherrors AT mghahramani shrinkageestimationoflinearregressionmodelswithgarcherrors |