Multi-modality in the Likelihood Function of GARCH Model

Farrukh Mahmood and Saud Ahmed Khan ()
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Farrukh Mahmood: Pakistan Institute of Development Economics, Pakistan
Saud Ahmed Khan: Pakistan Institute of Development Economics, Pakistan

Review of Pacific Basin Financial Markets and Policies (RPBFMP), 2020, vol. 23, issue 03, 1-23

Abstract: It is shown empirically that likelihood function of the GARCH is multi-modal. Hence, the maximum likelihood estimates at local and global maxima will be quantitatively different. Therefore, it is important to start an estimation method with consistent starting value that converge to global maxima. This study compares two estimation methods, BFGS and DE, on the basis of simulation and surface constructed by changing the value of GARCH (1,1) model. DE is superior and consistent throughout the surface, and across distributions. PSX is used as real-world application and it has been found that the estimates obtained from DE are best and unbiased.

Keywords: GARCH; maximum likelihood function; multi-modality; starting value (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219091520500186

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