GARCH-type models have been highly developed since Engle [1982] presented ARCH process 30 years ago. Different kinds of GARCH-type models are applicable to different kinds of research purposes. As documented by many literatures that short-memory processes with level shifts will exhibit properties that make standard tools conclude long-memory is present. Therefore, in this paper, we want to fore...

In financial modeling, it has been constantly pointed out that volatility clustering and conditional nonnormality induced leptokurtosis observed in high frequency data. Financial time series data are not adequately modeled by normal distribution, and empirical evidence on the non-normality assumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bol...

Article history: Received 10 May 2013 Received in revised form 2 September 2014 Accepted 2 September 2014 Available online 11 September 2014 The study investigates the relative performance of Value-at-Risk (VaR) models using daily share price index data from six different countries across Asia, Europe and the United States for a period of 10 years from January 01, 2000 toDecember 31, 2009. Them...

We revisit the risk-return relation using the component GARCH model and international daily MSCI stock market data. In contrast with the previous evidence obtained from weekly and monthly data, daily data show that the relation is positive in almost all markets and often statistically significant. Likelihood ratio tests reject the standard GARCH model in favor of the component GARCH model, whic...

This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...

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...

Environmental issues have become increasingly important in economic research and policy for sustainable development. Such issues are tracked by the Dow Jones Sustainable Indexes (DJSI) through financial market indexes that are derived from the Dow Jones Global Indexes. The environmental sustainability activities of firms are assessed using criteria in three areas, namely economic, environmental...

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment conditi...

Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previous...

In this paper the class of BL-GARCH (Bilinear General AutoregRessive Conditional Heteroskedasticity) models is introduced. The proposed model is a modification to the BL-GARCH model proposed by Storti and Vitale (2003). Stationary conditions and autocorrelation structure for special cases of these new models are derived. Maximum likelihood estimation of the model is also considered. Some simula...