On the parameter estimation of a new innovation distribution for GARCH (1,1) model
The autoregressive conditional heteroscedastic (ARCH) and generalized autoregressive conditional heteroscedastic (GARCH) models have been used for modelling the volatility of financial time series data. These models were developed under the assumption of a normal distribution for the innovation distribution. Due to some constraints of the normal distributions like being leptokurtic, some important features of a data cannot be captured. Other distributions for the innovation distribution have been developed over the years. This study proposes a new innovation (error) distribution which was obtained through a transformation function by converting the inverted exponentiated skewed student t distribution into an innovation distribution through a transformation function. The new innovation distribution was used on GARCH (1,1) model in order to obtain the volatility parameters. The volatility parameters were obtained by the method of maximum likelihood estimation. The shape and skewed parameters of this distribution were obtained as well. The proposed error distribution will serve as a competitor to existing error distributions with an improved form of flexibility that captures the attributes of financial assets’volatility behaviour.
Keywords: GARCH, inverted exponentiated skewed student t error distribution, maximum likelihood estimation, volatility
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