Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation
It is well known in the literature that obtaining the parameter estimates for the Smooth Transition Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) can be problematic due to computational difficulties. Conventional optimization algorithms do not seem to perform...
| Main Authors: | , |
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| Format: | Journal Article |
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Elsevier Science
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/30859 |
| _version_ | 1848753210248921088 |
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| author | Chan, Felix Theoharakis, Billy |
| author_facet | Chan, Felix Theoharakis, Billy |
| author_sort | Chan, Felix |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | It is well known in the literature that obtaining the parameter estimates for the Smooth Transition Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) can be problematic due to computational difficulties. Conventional optimization algorithms do not seem to perform well in locating the global optimum of the associated likelihood function. This makes Quasi-Maximum Likelihood Estimator (QMLE) difficult to obtain for STAR-GARCH models in practice. Curiously, there has been very little research investigating the cause of the numerical difficulties in obtaining the parameter estimates for STAR-GARCH using QMLE. The aim of the paper is to investigate the nature of the numerical difficulties using Monte Carlo Simulation. By examining the surface of the log-likelihood function based on simulated data, the results provide several insights into the difficulties in obtaining QMLE for STAR-GARCH models. Based on the findings, the paper also proposes a simple transformation on the parameters to alleviate these difficulties. Monte Carlo simulation results show promising signs for the proposed transform. The asymptotic and robust variance–covariance matrices of the original parameter estimates are derived as a function of the transformed parameter estimates, which greatly facilitates inferences on the original parameters. |
| first_indexed | 2025-11-14T08:20:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-30859 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:20:53Z |
| publishDate | 2011 |
| publisher | Elsevier Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-308592017-09-13T15:55:52Z Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation Chan, Felix Theoharakis, Billy Monte Carlo simulation GARCH STAR re-parameterization It is well known in the literature that obtaining the parameter estimates for the Smooth Transition Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) can be problematic due to computational difficulties. Conventional optimization algorithms do not seem to perform well in locating the global optimum of the associated likelihood function. This makes Quasi-Maximum Likelihood Estimator (QMLE) difficult to obtain for STAR-GARCH models in practice. Curiously, there has been very little research investigating the cause of the numerical difficulties in obtaining the parameter estimates for STAR-GARCH using QMLE. The aim of the paper is to investigate the nature of the numerical difficulties using Monte Carlo Simulation. By examining the surface of the log-likelihood function based on simulated data, the results provide several insights into the difficulties in obtaining QMLE for STAR-GARCH models. Based on the findings, the paper also proposes a simple transformation on the parameters to alleviate these difficulties. Monte Carlo simulation results show promising signs for the proposed transform. The asymptotic and robust variance–covariance matrices of the original parameter estimates are derived as a function of the transformed parameter estimates, which greatly facilitates inferences on the original parameters. 2011 Journal Article http://hdl.handle.net/20.500.11937/30859 10.1016/j.matcom.2010.05.023 Elsevier Science restricted |
| spellingShingle | Monte Carlo simulation GARCH STAR re-parameterization Chan, Felix Theoharakis, Billy Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title | Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title_full | Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title_fullStr | Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title_full_unstemmed | Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title_short | Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation |
| title_sort | estimating m-regimes star-garch model using qmle with parameter transformation |
| topic | Monte Carlo simulation GARCH STAR re-parameterization |
| url | http://hdl.handle.net/20.500.11937/30859 |