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 consider th e relationships between ARCH-type and stochast ic volatility models. A new class of volatility models, called generalized bilinear stochastic volatility, is described following an approach that tr ansforms an init ial GARCH-M process. Th e focus here is on th e interpretation of some simulation results, with a special care devoted to model misspecification.

This paper presents theoretical models and their empirical results for the return and variance dynamics of German stocks. A factor structure is used in order to allow for a parsimonious modeling of the rst two moments of returns. Dynamic factor models with GARCH dynamics (GARCH(1,1)-M, IGARCH(1,1)-M, Nonlinear Asymmetric GARCH(1,1)-M and Glosten-Jagannathan-Runkle GARCH(1,1)-M) and three di ere...

With the increase of wind power as a renewable energy source in many countries, wind speed forecasting has become more and more important to the planning of wind speed plants, the scheduling of dispatchable generation and tariffs in the day-ahead electricity market, and the operation of power systems. However, the uncertainty of wind speed makes troubles in them. For this reason, a wind speed f...

This paper derives asymptotic normality of a class of M-estimators in the generalized autoregressive conditional heteroskedastic ~GARCH! model+ The class of estimators includes least absolute deviation and Huber’s estimator in addition to the well-known quasi maximum likelihood estimator+ For some estimators, the asymptotic normality results are obtained only under the existence of fractional u...

Various e m p i r i d studies have shown that the time-varying volatility of asset returns can be described by GARCH (generalized autoregressive conditional heteroskedasticity) models. The corresponding GARCH option pricing model of Duan (1995) is capable of depicting the "smile-effect" which often can be found in option prices. In some derivative markets, however, the slope of the smile is not...

The role of price risk in sow farrowings is investigated by using bivariate ARCH-M and GARCH-M models and a nonparametric kernel estimator. To account for the relevant time horizon of irreversible supply decisions, predictions for mean price and conditional price variance are iterated forward. The empirical results vary markedly in terms of their implications for risk response in hog supply dec...

This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standard...

Financial returns are often modeled as autoregressive time series with innovations having conditional heteroscedastic variances, especially with GARCH processes. The conditional distribution in GARCH models is assumed to follow a parametric distribution. Typically, this error distribution is selected without justification. In this paper, we have applied the results of Thavaneswaran and Ghahrama...