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

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  • Chan, Felix
  • Theoharakis, Billy
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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  • Chan, Felix & Theoharakis, Billy, 2011. "Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1385-1396.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:7:p:1385-1396
    DOI: 10.1016/j.matcom.2010.05.023
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    References listed on IDEAS

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    1. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
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    Cited by:

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    5. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 173-200, September.
    6. Murat Midiliç, 2020. "Estimation of STAR–GARCH Models with Iteratively Weighted Least Squares," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 87-117, January.
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    9. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    10. Novella Maugeri, 2014. "Some Pitfalls in Smooth Transition Models Estimation: A Monte Carlo Study," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 339-378, October.
    11. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2023. "Building Multivariate Time-Varying Smooth Transition Correlation GARCH Models, with an Application to the Four Largest Australian Banks," Econometrics, MDPI, vol. 11(1), pages 1-37, February.
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