The generalized autoregressive conditional heteroscedasticity (GARCH) approach is one of the common and simpler ways to use historical data to produce estimates of current and future levels of volatilities. This model recognizes that volatilities are not constant, for instance, a particular volatility may be high or low depending on the period of time. One of goals of a GARCH model is to track ...

This article discusses the application of Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) time series models for representing the dynamics of traffic flow volatility. The methods encountered in the literature so far, focus on the levels of traffic flows while regarding variance constant through time. The approach adopted in this paper concentrates mostly on the autoregressive...

Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised ex...

In this paper, we introduce a two−dimensional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model for clutter modeling and anomaly detection. The one−dimensional GARCH model is widely used for modeling financial time series. Extending the one−dimensional GARCH model into two dimensions yields a novel clutter model which is capable of taking into account important characteris...

The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH parameters correctly. The algorithm is rather general and it can be applied to other ...

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...

The volatility clustering frequently observed in financial/economic time series is often ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the usefulness of reconceptualizing the usual definition of conditional heteroscedasticity as the (h = 1) special case of h-step-ahead conditional heteroscedasticity, where the conditional volatility in period t depends on observ...

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here...

this paper investigates the relationship between inflation and growth uncertainty in iran for the period of 1988-2008 by using quarterly data. we employ generalized autoregressive conditional heteroscedasticity in mean (garch-m) model to estimate time-varying conditional residual variance of growth, as a standard measures of growth uncertainty. the empirical evidence shows that growth uncertain...

Unobserved component models with GARCH disturbances are extended to allow for asymmetric responses of conditional variances to positive and negative shocks. The asymmetric conditional variance is represented by a member of the QARCH class of models. The proposed model allows to distinguish whether the possibly asymmetric conditional heteroscedasticity affects the short-run or the long-run distu...