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...

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded t...

While ARCH/GARCH equations have been widely used to model financial market data, formal explanations for the sources of conditional volatility are scarce. This paper presents a model with the property that standard econometric tests detect ARCH/GARCH effects similar to those found in asset returns. We use evolutionary game theory to describe how agents endogenously switch among different foreca...

This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

I n this paper, we specify that the GARCH(1,1) model has strong forecasting volatility and its usage under the truncated standard normal distribution (TSND) is more suitable than when it is under the normal and student-t distributions. On the contrary, no comparison was tried between the forecasting performance of volatility of the daily return series using the multi-step ahead forec...

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for geometric ergodicity and existence of moments. Because of path dependence, maximum likelihood estimation is no...

Factor models are well established as promising alternatives to obtain covariance matrices of portfolios containing a very large number of assets. In this paper, we consider a novel multivariate factor GARCH specification with a flexible modeling strategy for the common factors, for the individual assets, and for the factor loads. We apply the proposed model to obtain minimum variance portfolio...

In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for GARCH models. Previous studies show that maximum likelihood estimates of GARCH models are sensitive to outliers and financial time series present a heavy tail due to outliers. The proposed BIE limits the influence of a small subset of the data and is asymptotically normal. Its robustness against o...

Methods: One commodity future from each group of futures is chosen for the analysis. The select commodities are potato, gold, crude oil, and mentha oil. The data are collected from MCX India over the period 2004–2012. This study uses several econometric techniques for the analysis. The GARCH model is introduced for examining the volatility of commodity futures. One of the key contributions of t...

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 ...