We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled co...

We consider the parameter restrictions that need to be imposed in order to ensure that the conditional variance process of a GARCH(p, q) model remains non-negative. Previously, Nelson and Cao (1992) provided a set of necessary and sufficient conditions for the aforementioned non-negativity property for GARCH(p, q) models with p ≤ 2, and derived a sufficient condition for the general case of GAR...

In the presence of generalized conditional heteroscedasticity (GARCH) in the residuals of a vector error correction model (VECM), maximum likelihood (ML) estimation of the cointegration parameters has been shown to be efficient. On the other hand, full ML estimation of VECMs with GARCH residuals is computationally difficult and may not be feasible for larger models. Moreover, ML estimation of V...

GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years ago by Klüppelberg, Lindner and Maller, and Nelson’s diffusion limit are the only functional continuous-time limits of GARCH in distribution. In contrast to Nelson’s diffusion limit, COGARCH reprodu...

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...

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major c...

A simple iterative algorithm for nonparametric 1rst-order GARCH modelling is proposed. This method o4ers an alternative to 1tting one of the many di4erent parametric GARCH speci1cations that have been proposed in the literature. A theoretical justi1cation for the algorithm is provided and examples of its application to simulated data from various stationary processes showing stochastic volatili...