Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models

Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a equence of steps following the Hamiltonian dynamics of the underlying parameter space, often yielding superior mixing properties of the resulting Markov chain. However, its performance can deteriorate sharply with the degree of irregularity of the underlying likelihood due to its lack of local adaptability in the parameter space. Riemann Manifold HMC (RMHMC), a locally adaptive version of HMC, alleviates this problem, but at a substantially increased computational cost that can become prohibitive in high-dimensional scenarios. In this paper we propose the Adaptive HMC (AHMC), an alternative inferential method based on HMC that is both fast and locally adaptive, combining the advantages of both HMC and RMHMC. The benefits become more pronounced with higher dimensionality of the parameter space and with the degree of irregularity of the underlying likelihood surface. We show that AHMC satisfies detailed balance for a valid MCMC scheme and provide a comparison with RMHMC in terms of effective sample size, highlighting substantial efficiency gains of AHMC. Simulation examples and an application of the BEKK GARCH model show the usefulness of the new posterior sampler.High-dimensional joint sampling; Markov chain Monte Carlo; Multivariate GARCH

Modelling Realized Covariances and Returns

This paper proposes new dynamic component models of returns and realized covariance (RCOV) matrices based on time-varying Wishart distributions. Bayesian estimation and model comparison is conducted with a range of multivariate GARCH models and existing RCOV models from the literature. The main method of model comparison consists of a term-structure of density forecasts of returns for multiple forecast horizons. The new joint return-RCOV models provide superior density forecasts for returns from forecast horizons of 1 day to 3 months ahead as well as improved point forecasts for realized covariances. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out.Wishart distribution, predictive likelihoods, density forecasts, MCMC

Modelling Realized Covariances and Returns

This paper proposes new dynamic component models of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications are linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. The models are compared based on a term-structure of density forecasts of returns for multiple forecast horizons. Relative to multivariate GARCH models that use only daily returns, the joint RCOV and return models provide significant improvements in density forecasts from forecast horizons of 1 day to 3 months ahead. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out.eigenvalues, dynamic conditional correlation, predictive likelihoods, MCMC

Modelling Realized Covariances

This paper proposes a new dynamic model of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications can be linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast. Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. We extend the model to capture the strong persistence properties in RCOV. Out-of-sample performance based on statistical and economic metrics show the importance of this. We discuss which features of the model are necessary to provide improvements over a traditional multivariate GARCH model that only uses daily returns.eigenvalues, dynamic conditional correlation, predictive likelihoods, MCMC

Bayesian Semiparametric Stochastic Volatility Modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility modelsClassification-JEL:

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns

This paper models different components of the return distribution which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. This mixture captures occasional large changes in price, due to the impact of news innovations such as earnings surprises, as well as smoother changes in prices which can result from liquidity trading or strategic trading as information disseminates. Unlike typical SV-jump models, previous realizations of both jump and normal innovations can feedback asymmetrically into expected volatility. This is a new source of asymmetry (in addition to good versus bad news) that improves forecasts of volatility particularly after large moves such as the '87 crash. A heterogeneous Poisson process governs the likelihood of jumps and is summarized by a time varying conditional intensity parameter. The model is applied to returns from individual companies and three indices. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, contemporaneous and lagged leverage effects, the time-series dynamics of jump clustering, and the importance of modeling the dynamics of jumps around high volatility episodes. Cet article modélise les différentes composantes de la distribution des rendements qui sont supposés être régis par un processus latent de nouvelles. La variance conditionnelle des rendements est une combinaison de sauts et de composantes qui varient continûment. Ce mélange permet de capter les grands changements occasionnels de prix qui sont dus à l'impact des nouvelles, telles que des surprises dans les revenus d'une compagnie, aussi bien que des changements plus lisses des prix qui peuvent résulter de transactions de liquidité ou de transactions stratégiques au fur et à mesure que l'information est disséminée. À la différence des modèles classique de sauts SV, les réalisations précédentes des sauts et des innovations normales peuvent intervenir asymétriquement dans la volatilité espérée. Il s'agit d'une nouvelle source d'asymétrie qui améliore les prévisions de volatilité, en particulier après de grands mouvements tels que le crash de 87. Un processus de Poisson hétérogène régit la probabilité des sauts et est représenté par un paramètre d'intensité conditionnelle qui varie dans le temps. Le modèle est appliqué aux rendements de différentes compagnies et à trois indices. Nous montrons ainsi empiriquement l'impact et les effets de rétroaction des sauts par rapport aux innovations normales, les effets de leviers simultanés et décalés, la dynamique de série temporelle du groupement des sauts, et l'importance de modéliser la dynamique des sauts dans les périodes de volatilité élevée.volatility components, news impacts, conditional jump intensity, jump size, leverage effects, filter, composantes de volatilité, impact des nouvelles, intensité conditionnelle des sauts, taille des sauts, effets de levier, filtre

Nonlinear Features of Realized FX Volatility

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives. Dans cet article, nous étudions les caractéristiques nonlinéaires de la dynamique de la volatilité des taux de change à l'aide d'estimations de la volatilité quotidienne basées sur la somme du carré des rendements intraquotidiens. Les erreurs de mesure commises en utilisant la volatilité réalisée pour mesurer la volatilité latente ex post font en sorte que les modèles standards de séries chronologiques de la variance conditionnelle deviennent des variantes d'un modèle ARMAX. Nous explorons des alternatives nonlinéaires à ces spécifications linéaires en utilisant un processus doublement stochastique, avec mixage dépendant de la durée. Ce processus peut capter des changements importants et abrupts dans le niveau de la volatilité, de même qu'une persistence et une variance de la volatilité variant dans le temps. Nos résultats influent sur la précision des prévisions, la couverture et l'évaluation des produits dérivés.High-frequency data, realized volatility, semi-Marko, Données à haute fréquence, volatilité réalisée, demi-Markov

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, we use nonparametric Bayesian methods to flexibly model the skewness and kurtosis of the distribution while continuing to model the dynamics of volatility with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. We present a Markov chain Monte Carlo sampling approach to estimation with theoretical and computational issues for simulation from the posterior predictive distributions. The new model is assessed based on simulation evidence, an empirical example, and comparison to parametric models.Econometric models ; Stochastic analysis

Les transferts linguistiques au Québec entre 1975 et 1977

Le nouveau formulaire de déclaration de naissance en usage au Québec depuis juin 1975 comporte des questions sur la langue maternelle du père et de la mère ainsi que sur la principale langue d’usage à la maison de la mère. On dispose donc d’une source de renseignements sur les transferts linguistiques entre les recensements décennaux. Les données des années 1975 à 1977 révèlent une situation assez semblable à celle observée au recensement de 1971. Des liens importants sont établis entre les transferts linguistiques et l’exogamie linguistique. Le comportement de divers sous-ensembles de la population est passé en revue