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...

Detecting and modelling structural changes in GARCH processes have attracted a great amount of attention in time series econometrics over the past few years. In this paper, we …rst generalize Dahlhaus and Subba Rao (2006 2008)’s time-varying ARCH processes to time-varying GARCH processes and derive the consistency and asymptotic normality of the weighted quasi maximum likelihood estimator of th...

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...

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the leastsquares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process ...

This paper focuses on the performance of various GARCH models in terms of their ability of delivering volatility forecasts for stock return data. Volatility forecasts obtained from a variety of mean and variance specifications in GARCH models are compared to a proxy of actual volatility calculated using daily data. In-sample tests suggest that a regression of volatility estimates on actual vola...