In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persisten...

It is a well-known fact that financial returns exhibit conditional heteroscedasticity and fat tails. While the GARCH-type models are very popular in depicting the conditional heteroscedasticity, the α-stable distribution is a natural candidate for the conditional distribution of financial returns. The α-stable distribution is a generalization of the normal distribution and is described by four ...

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models...

Modelling and detecting structural changes in GARCH processes have attracted a great amount of attention in econometrics over the past few years. We generalize Dahlhaus and Rao (2006)’s time varying ARCH processes to time varying GARCH processes and show the consistency of the weighted quasi maximum likelihood estimator. A class of generalized likelihood ratio tests are proposed to check smooth...

Modeling financial volatility is an important part of empirical finance. This paper provides a literature review of the most relevant volatility models, with a particular focus on forecasting models. We firstly discuss the empirical foundations of different kinds of volatility. The paper, then, analyses the non-parametric measure of volatility, named realized variance, and its empirical applica...

This paper derives asymptotic normality of a class of M-estimators in the generalized autoregressive conditional heteroskedastic ~GARCH! model+ The class of estimators includes least absolute deviation and Huber’s estimator in addition to the well-known quasi maximum likelihood estimator+ For some estimators, the asymptotic normality results are obtained only under the existence of fractional u...

a for forecasting purposes arises from the fact that this conditional mean is allowed to be a random varible which depends on the available data, and evolves with time. The conditional variance, however, is r simply var [x e x ] = var [ε ] =σ , which remains constant regardless of the given data. Thus, the linea t t −1 t ε AR (1) model fails to adequately describe the conditional variance. In p...

Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study esti...

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...

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...