Aggregations and Marginalization of GARCH and Stochastic Volatility Models

The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions, thanks to a state-space setting, we obtain aggregation results without renouncing to the conditional variance concept (and related leverage effects), as it is the case for the recently suggested weak GARCH model which gets aggregation results by replacing conditional expectations by linear projections on symmetric past innovations. Moreover, unlike the weak GARCH literature, we are able to define multivariate models, including higher order dynamics and risk premiums (in the spirit of GARCH (p,p) and GARCH in mean) and to derive conditional moment restrictions well suited for statistical inference. Finally, we are able to characterize the exact relationships between our SR-SARV models (including higher order dynamics, leverage effect and in-mean effect), usual GARCH models and continuous time stochastic volatility models, so that previous results about aggregation of weak GARCH and continuous time GARCH modeling can be recovered in our framework.

Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Les pratiques pédagogiques exemplaires en sciences de l'information : 21 fiches annotées

Ce rapport constitue une version augmentée d’un premier rapport datant d’août 2005. Les 21 fiches annotées peuvent aussi être consultées individuellement (en format HTML) à partir du « Portail des ressources pédagogiques et disciplinaires en sciences de l'information » accessible à l’adresse : http://www.ebsi.umontreal.ca/clip/

Association between disruption of CD4 receptor dimerization and increased human immunodeficiency virus type 1 entry

Affiliation: Département de microbiologie et immunologie, Faculté de médecine, Université de Montréal & Institut de Recherches Cliniques de Montréal

Contribution of the C-terminal tri-lysine regions of human immunodeficiency virus type 1 integrase for efficient reverse transcription and viral DNA nuclear import

Affiliation: Zhujun Ao, Éric Cohen & Xiaojian Yao : Département de microbiologie et immunologie, Faculté de Médecine, Université de Montréal

Analysis of HIV-1 Vpr determinants responsible for cell growth arrest in Saccharomyces cerevisiae

Affiliation: Département de microbiologie et immunologie, Faculté de médecine, Université de Montréal

Can business & monetary conditions predict variations in expected stock returns?

Rapport de recherche

La variabilité du taux de change réel : incidence sur la PPA.

Rapport de recherche

Maîtrise du risque et évolution de l'outil informatique à la Banque Royale du Canada.

Rapport de recherche

Stochastic Volatility.

This paper prepared for the Handbook of Statistics (Vol.14: Statistical Methods in Finance), surveys the subject of stochastic volatility. the following subjects are covered: volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and, finally, statistical inference (methods of moments, quasi-maximum likelihood, likelihood-based and bayesian methods and indirect inference).