Denis Pelletier

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.

Simulation smoothing for state-space models: A computational efficiency analysis

Simulation smoothing involves drawing state variables (or innovations) in discrete time state-space models from their conditional distribution given parameters and observations. Gaussian simulation smoothing is of particular interest, not only for the direct analysis of Gaussian linear models, but also for the indirect analysis of more general models. Several methods for Gaussian simulation smoothing exist, most of which are based on the Kalman filter. Since states in Gaussian linear state-space models are Gaussian Markov random fields, it is also possible to apply the Cholesky Factor Algorithm (CFA) to draw states. This algorithm takes advantage of the band diagonal structure of the Hessian matrix of the log density to make efficient draws. We show how to exploit the special structure of state-space models to draw latent states even more efficiently. We analyse the computational efficiency of Kalman-filter-based methods, the CFA, and our new method using counts of operations and computational experiments. We show that for many important cases, our method is most efficient. Gains are particularly large for cases where the dimension of observed variables is large or where one makes repeated draws of states for the same parameter values. We apply our method to a multivariate Poisson model with time-varying intensities, which we use to analyse financial market transaction count data.

Nonnested Testing In Models Estimated Via Generalized Method Of Moments

Rivers and Vuong (2002) develop a very general framework for choosing between two competing dynamic models. Within their framework, inference is based on a statistic that compares measures of goodness of fit between the two models. The null hypothesis is that the models have equal measures of goodness of fit; one model is preferred if its goodness of fit is statistically significantly smaller than its competitor. Under the null hypothesis, Rivers and Vuong (2002) show that their test statistic has a standard normal distribution under generic conditions that are argued to allow for a variety of estimation methods including Generalized Method of Moments (GMM). In this paper, we analyze the limiting distribution of Rivers and Vuongs (2002) statistic under the null hypothesis when inference is based on a comparison of GMM minimands evaluated at GMM estimators. It is shown that the limiting behaviour of this statistic depends on whether the models in question are correctly specified, locally misspecified or misspecified. Specifically, it is shown that: (i) if both models are correctly specified or locally misspecified then Rivers and Vuongs (2002) generic conditions are not satisfied, and the limiting distribution of the test statistic is non-standard under the null; (ii) if both models are misspecified then the generic conditions are satisfied, and so the statistic has a standard normal distribution under the null. In the latter case it is shown that the choice of weighting matrices affects the outcome of the test and thus the ranking of the models.