This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...

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 major condition that is often used in proving the consistency of QML, the correct specification of t...

The paper studies a factor GARCH model and develops test procedures which can be used to test the number of factors needed to model the conditional heteroskedasticity in the considered time series vector. Assuming normally distributed errors the parameters of the model can be straightforwardly estimated by the method of maximum likelihood. Inefficient but computationally simple preliminary esti...

This paper proposes a threshold multivariate GARCH model (Threshold MGARCH) which integrates threshold nonlinearity, mean and volatility asymmetries and time-varying correlation in financial markets. The main feature of this model is that the mean, volatility and time-varying correlation can be governed by different threshold variables with different number of regimes. Estimation is performed u...

In this paper we present a new type of multivariate GARCH model which we call the composed MGARCH and factor composed MGARCH models. We show sufficient conditions for the covariance stationarity of these processes and proof of the invariance of the models under linear combinations, an important property for factor modeling. Furthermore, we introduce an α-stable version of these models and fit a...