In this paper we consider a general ...rst-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for ...rstorder exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checkin...

Volatility modelling of asset returns is an important aspect for many financial applications, e.g., option pricing and risk management. GARCH models are usually used to model the volatility processes of financial time series. However, multivariate GARCH modelling of volatilities is still a challenge due to the complexity of parameters estimation. To solve this problem, we suggest using Independ...

We analyze the time-dependence of exchange rate correlations using a new multivariate GARCH model. This model consists of two parts. First, we transform the exchange rate changes into their principal components and specify univariate GARCH models for all components. Second, we use the inverse of the principal components construction to transform the conditional component moments back into those...

It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average w...

Correlations among the asset returns are the main reason for the computational and statistical complexities of the full multivariate GARCH models. We rely on the variancecorrelation separation strategy and introduce a broad class of multivariate models in the spirit of Engle’s (2002) dynamic conditional correlation models, that is univariate GARCH models are used for variances of individual ass...

Several aspects of GARCH(p, q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A re...

We introduce a new framework, Realized GARCH, for the joint modeling of returns and realized measures of volatility. A key feature is a measurement equation that relates the realized measure to the conditional variance of returns. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility. Realized GARCH models with a linear or log-linear spec...

Correlations among the asset returns are the main reason for the computational and statistical complexities of the full multivariate GARCH models. We rely on the variancecorrelation separation strategy and introduce a broad class of multivariate models in the spirit of Engle’s (2002) dynamic conditional correlation models, that is univariate GARCH models are used for variances of individual ass...

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...