Power transformation in quasi-likelihood innovations for GARCH volatility

Abstract

This paper is concerned with power transformations in estimating GARCH volatility. To handle a semiparametric case for which the exact likelihood is not known, quasi-likelihood (QL) rather than maximumlikelihood method is investigated to best estimate GARCH via maximizing the information criteria. A power transformation is introduced in the innovation generating QL estimating functions and then optimum power is selected by maximizing the profile information. A combination of two different power transformations is also studied in order to increase the parameter estimation efficiency. Nine domestic stock prices data are analyzed to order to illustrate the main idea of the paper. The data span includes Covid-19 pandemic period in which financial time series are really volatile.