We present a unified and up-to-date overview of temporal aggregation techniques for univariate and multivariate time series models explaining in detail how these techniques are employed. Some empirical applications illustrate the main issues.

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak multivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low...

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and - mixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated...

In the empirical analysis of financial time series, multivariate GARCH models have been used in various forms. As it is typical for nonlinear models there is yet no unique framework available to uncover dynamic covariance relationships for vector return processes. We introduce a new concept of...

This paper investigates the performance of quasi maximum likelihood (QML) and nonlinear least squares (NLS) estimation applied to temporally aggregated GARCH models. Since these are known to be only weak GARCH, the conditional variance of the aggregated process is in general not known. Thus, one...

The volatility accuracy of several volatility forecast models is examined for the case of daily spot returns for the Mexican peso - US Dollar exchange rate. The models applied are univariate GARCH, a multi-variate GARCH (the BEKK model), option implied volatilities, and a composite forecast...

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...

We study the joint movements of the returns on futures for crude oil, heating oil and natural gas at a daily frequency. We model the leptokurtic behavior through the multivariate GARCH with dynamic conditional correlations and elliptical distributions introduced by Pelagatti and Rondena (2004)....