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Define GARCH
GARCH allows the estimation of univariate as well as multivariate non-parametric estimators of the quadratic variation and the integrated volatility as these estimators include the realized volatility as well as bi-power-variation and realized Outlyingness weighted variance.
Several tests for daily tests for jumps and intraday periodicity filters are also provided and this is a software that is dedicated to the estimation and the forecasting of univariate as well as multivariate GARCH models and many of their extensions. It can be used along within OxMetrics via the classic programming way using the OxEdit for instance for those who have access to the Ox programming language.
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The available univariate models are all ARCH-type models as these include ARCH and GARCH as well as EGARCH and GJR. It also includes models like APARCH and IGARCH as well as RiskMetrics and FIGARCH.
The other models are FIEGARCH and FIAPARCH as well as HYGARCH. They can be estimated by approximate (Quasi-) Maximum Likelihood under one of the four proposed distributions for the errors and moreover, ARCH-in-mean models are also available. The explanatory variables can enter the conditional mean and/or the conditional variance equations.
It also proposes some multivariate GARCH specifications including the scalar BEKK and diagonal BEKK as well as full BEKK and Risk Metrics. The other specifications are CCC and DCC as well as DECO and OGARCH and GOGARCH models. h-steps-ahead forecasts of both equations are available as well as many univariate and multivariate miss-specification tests such as Nyblom and Sign Bias Tests, Pearson goodness-of-fit as well as Box-Pierce and Residual-Based Diagnostic for conditional heteroscedasticity.
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The other specification test includes Hosking’s portmanteau test and Li and McLead's test as well as the constant correlation test. It cannot operate without data and so once the OxMetrics is activated, the very first step is to load data and provides several tests on the raw data in addition to the possibilities offered by OxMetrics such as ACF and PACF as well as QQ-plots.
It provides three methods to compute the covariance matrix of the estimates such as the Second Derivatives which is based on the inverse of the Hessian, the Outer-Product of Gradients Robust standard errors which are also known as Quasi-Maximum Likelihood. This choice is accessible by clicking on the button ‘Options...’ and by default, Robust standard errors are reported.
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