Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation
✍ Scribed by Felix Chan; Billy Theoharakis
- Book ID
- 104042671
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 358 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0378-4754
No coin nor oath required. For personal study only.
✦ Synopsis
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.