Estimate the parameters of the GARCH model for the Hyperbolic Secant Distribution with the application
Keywords:
: ARCH , Brent Oil Prices , Hyperbolic Secant Distribution , Model selectionAbstract
The study of AutoRegressive Conditional Heteroscedasticity models of the important studies in time series, especially financial ones, because most of the financial time series have high Volatility that is, the conditional variance in them is not fixed and depends on the past, that most of the previous studies rely on some distributions such as normal distribution GED distribution and t distribution.
In this paper, a new distribution of the GARCH model, which is hyperbolic- secant distribution , is presented in theory and practice. A sample representing the opening price of the Brent oil was found and the data test showed that it follows the hyperbolic secant distribution. After testing it was found to be a problem for ARCH. After estimating it was found that the best model to represent this data according to the best test criteria is AIC, SIC, H-Q, GARCH (1 , 1).
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