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    Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation

    Access Status
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    Authors
    Chan, Felix
    Theoharakis, Billy
    Date
    2011
    Type
    Journal Article
    
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    Citation
    Chan, Felix and Theoharakis, Billy. 2011. Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation. Mathematics and Computers in Simulation. 81 (7): pp. 1385-1396.
    Source Title
    Mathematics and Computers in Simulation
    DOI
    10.1016/j.matcom.2010.05.023
    ISSN
    0378-4754
    School
    School of Economics and Finance
    URI
    http://hdl.handle.net/20.500.11937/30859
    Collection
    • Curtin Research Publications
    Abstract

    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.

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