2016 |
Delaigle, Aurore; Meister, Alexander; Rombouts, Jeroen V. K. Root-T consistent density estimation in GARCH models Journal Article In: Forthcoming in the Journal of Econometrics, vol. Volume 192, Issue 1, pp. 55-63, 2016. Abstract | Links | BibTeX | Tags: Garch @article{JR-Journal5t,We consider a new nonparametric estimator of the stationary density of the logarithm of the volatility of the GARCH( 1,1) model. This problem is particularly challenging since this density is still unknown, even in cases where the model parameters are given. Although the volatility variables are only observed with multiplicative independent innovation errors with unknown density, we manage to construct a nonparametric procedure which estimates the log volatility density consistently. By carefully exploiting the specific GARCH dependence structure of the data, our iterative procedure even attains the striking parametric root- T convergence rate. As a by-product of our main results, we also derive new smoothness properties of the stationary density. Using numerical simulations, we illustrate the performance of our estimator, and we provide an application to financial data. |
2014 |
Bauwens, Luc; Arnaud, Dufays; Rombouts, Jeroen V. K. Marginal Likelihood Computation for Markov Switching and Change-point GARCH Models Journal Article In: Journal of Econometrics, vol. Volume 178, Issue P3, pp. 508-522, 2014. Abstract | Links | BibTeX | Tags: Garch @article{JR-Journal5r,GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu et al. (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series. |
2012 |
Laurent, Sébastien; Rombouts, Jeroen V. K.; Violante, Francesco On the Forecasting Accuracy of Multivariate GARCH Models Journal Article In: Journal of Applied Econometrics, vol. Volume 27, Issue 6, pp. 934–955, 2012. Abstract | Links | BibTeX | Tags: Forecasting , Garch @article{JR-Journal5n,This paper addresses the question of the selection of multivariate generalized autoregressive conditional heteroskedastic (GARCH) models in terms of variance matrix forecasting accuracy, with a particular focus on relatively large-scale problems. We consider 10 assets from the New York Stock Exchange and compare 125 models based 1-, 5- and 20-day-ahead conditional variance forecasts over a period of 10 years using the model confidence set (MCS) and the superior predictive ability (SPA) tests. Model performance is evaluated using four statistical loss functions which account for different types and degrees of asymmetry with respect to over-/under-predictions. When considering the full sample, MCS results are strongly driven by short periods of high market instability during which multivariate GARCH models appear to be inaccurate. Over relatively unstable periods, i.e. the dot-com bubble, the set of superior models is composed of sophisticated specifications such as orthogonal and dynamic conditional correlation (DCC), both with leverage effect in the conditional variances. However, unlike the DCC models, our results show that the orthogonal specifications tend to underestimate the conditional variance. Over calm periods, a simple assumption like constant conditional correlation and symmetry in the conditional variances cannot be rejected. Finally, during the 2007–2008 financial crisis, accounting for non-stationarity in the conditional variance process generates superior forecasts. The SPA test suggests that, independently from the period, the best models do not provide significantly better forecasts than the DCC model of Engle. |
2010 |
Bauwens, Luc; Preminger, Arie; Rombouts, Jeroen V. K. Theory and Inference for a Markov Switching GARCH Model Journal Article In: The Econometrics Journal , pages, July 2010, vol. Volume 13, Issue 2, pp. 218–244, 2010. Abstract | Links | BibTeX | Tags: Garch @article{JR-Journal5j,We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on S&P500 daily returns. |
2009 |
Rombouts, Jeroen V. K.; Verbeek, Marno Evaluating Portfolio Value-at-Risk using Semi-parametric GARCH Models Journal Article In: Quantitative Finance , vol. Volume 9, Issue 6, 2009. Abstract | Links | BibTeX | Tags: Garch @article{JR-Journal5e,In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within-sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. |