To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standa...

4 GARCH Models 7 4.1 Basic GARCH Specifications . . . . . . . . . . . . . . . . . . . 8 4.2 Diagnostic Checking . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Regressors in the Variance Equation . . . . . . . . . . . . . . . 12 4.4 The GARCH–M Model . . . . . . . . . . . . . . . . . . . . . . 12 4.5 The Threshold GARCH (TARCH) Model . . . . . . . . . . . . 12 4.6 The Exponential GARCH (EG...

We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled co...

The study has two aims. The first aim is to propose a family of nonlinear GARCH models that incorporate fractional integration and asymmetric power properties to MS-GARCH processes. The second purpose of the study is to augment the MS-GARCH type models with artificial neural networks to benefit from the universal approximation properties to achieve improved forecasting accuracy. Therefore, the ...

The skewness in physical distributions of equity index returns and the implied volatility skew in the risk neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introd...