ARCH and GARCH models have been used recently in model-based signal processing applications, such as speech and sonar signal processing. In these applications, additive noise is often inevitable. Conventional methods for parameter estimation of ARCH and GARCH processes assume that the data are clean. The parameter estimation performance degrades greatly when the measurements are noisy. In this ...

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter...

We address the IGARCH puzzle, by which we understand the fact that a GARCH(1,1) model fitted to virtually any financial dataset exhibit the property thatˆα + ˆ β is close to one. We do this by proving that if data is generated by a stochastic volatility model but fitted to a GARCH(1,1) model one would get thatˆα + ˆ β tends to one in probability as the sampling frequency is increased. We also d...

Although the GARCH model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and lepto...

This paper proposes a new parametric volatility model that introduces serially dependent innovations in GARCH specifications. We first prove the asymptotic normality of the QML estimator in this setting, allowing for possible explosive and nonstationary behavior of the GARCH process. We show that this model can generate an alternative measure of risk premium relative to the GARCH-M. Finally, we...

Traditional GARCH models describe volatility levels that evolve smoothly over time, generated by a single GARCH regime. However, nonstationary time series data may exhibit abrupt changes in volatility, suggesting changes in the underlying GARCH regimes. Further, the number and times of regime changes are not always obvious. This article outlines a nonparametric mixture of GARCH models that is a...

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...

This paper develops a parametric family of models of generalized autoregressive heteroscedasticity (garch). The family nests the most popular symmetric and asymmetric garch models, thereby highlighting the relation between the models and their treatment of asymmetry. Furthermore, the structure permits nested tests of different types of asymmetry and functional forms. U.S. stock return data reje...

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal ...

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...