Using Linear Wavelets in Analyzing the GARCH Model with the Simulation

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Using Linear Wavelets in Analyzing the GARCH Model with the Simulation

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Abstract

In this research, it was proposed to use linear wavelet shrinkage to reduce the noise in the data of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, which relies on time series data that is not homogeneous in variance, through the use of several linear wavelets, specifically Daubechies, Coiflets, and Dmey of the first order, to maintain the same order as the classical GARCH model, which is suitable for those data by estimating the thresholding level using the Minimax method and applying the soft threshold rule to obtain de- noise data and then using it to estimate the parameters of the GARCH models and comparing it with classical GARCH models that rely on the original data and without adding any percentages of contamination to the data in simulation experiments or real data. Comparison of the efficiency of the estimated models is based on the Akaike and Bayes information criterion through a MATLAB program designed for this purpose. The research results revealed that the GARCH models estimated using the proposed method were more efficient than the GARCH models estimated using the classical method, in addition to the Dmey wavelet being superior to the rest of the linear wavelets used in the research.

Keywords

Time Series GARCH Model Linear Wavelet Threshold Soft Rule.

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