We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...

In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly ...

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...

The goal of this study was to identify a reliable GARCH model for modeling and forecasting each economic variable in Nigeria, including the price crude oil, consumer index, exchange rate, inflation rate. Monthly secondary data simulated sets were that used. Between January 2004 December 2020, are covered. Beta Volatility Coefficient (BVC) proposed detecting volatility research data. Using metho...

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 dealt with the autoregressive model when coefficient is random. The residuals series of exhibit two behaviors, kurtosis and volatility. These volatilities are usually seasonal in real financial data, which always uses GARCH models. So use RCA models together will provide an appropriate framework to study analysis time-varying volatility as well presence effects series. Applying coppe...