||This study attempts to capture the behavior of volatility in the commodity futures market by importing the normal mixture GARCH Model and the NIG mixture GARCH model (Normal-inverse Gaussian Mixture GARCH Model). Normal mixture GARCH Model (what follows called NM-GARCH Model) is a model mixed by two to several normal distributions with a specific weight portfolio, and its variance abide by GAECH process. The ability of capturing the financial data with leptokurtosis and fat-tail of NM-GARCH Model is better than Normal GARCH Model and Student’s t GARCH Model.。Also，The Variance of the factor with lower weight in NM-GARCH Model usually higher, and the volatility of the factor with higher weight is lower, which explains the situation happens in the real market that the probability of large fluctuations (shocks) is small, and the probability of small fluctuations are higher. Generally, the volatilities which keeping occurring in common cases are respectively flat, and the shocks usually bring large impacts but less frequent. |
NIG Mixture Distribution is a distribution mixed by two to several weighted distributions, and the distribution of every factor abides by NIG Distribution. Compare to Normal Mixture Distribution, NIG Mixture Distribution takes the advantages of NIG Distribution into account, which can not only explain leptokurtosis and the deviation of data, but describe the fat-tail phenomenon more complete as well, because of the both tails of NIG Distribution decreasing slowly.
This study will apply the NM GARCH Model and NIG GARCH Model to the Volatility forecasting of the return rates in the crude oil futures market, and infer the predictive abilities of this two kinds of models are significantly better than other volatility model by implementing parameter estimation, forecasting, loss function and statistic significant test.
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