In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AO's). We show analytically that both the asymptotic size and power are adversely aaected if AO's are neglected: the test rejects the null hypothesis of homoskedasticity too often when it is i...

The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BLGARCH model proposed by Storti and Vitale (2003a; 2003b). It is shown how MBL-GARCH models allow to account for asymmetric effects in both conditional variances and correlations. An EM...

A new variant of the ARCH class of models for forecasting conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) Model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the Realized Volatility that requires a large amount of intra-daily data, which remain relatively costly and are...

GARCH models with Markov-switching regimes are often used for volatility analysis of …nancial time series. Such models imply less persistence in the conditional variance than the standard GARCH model, and potentially provide a signi…cant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this...

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our “COGARCH” (continuous time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous time stochast...

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...

It has become common practice to fit GARCH models to financial time series by means of pseudo maximum likelihood. In this study we investigate the behaviour of several maximum likelihood based methods for estimating the Garch model parameters and for estimating volatility and risk measures (VaR and expected shortfall). We consider NIG, skewed-t, t and nonparametric kernel densities for this pur...

98. Nelson DB (1990) Stationarity and persistence in the GARCH(1,1) model. Econom Theory 6:318–334 99. Nelson DB (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59:347–370 100. Nelson DB, Cao CQ (1992) Inequality constraints in the univariate garchmodel. J Bus Econ Stat 10:229–235 101. Newey WK, Steigerwald DS (1997) Asymptotic bias for quasi maximum likelih...