Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.

Modelos dinâmicos e simulação estocástica

This paper presents new methodology for making Bayesian inference about dy~ o!s for exponential famiIy observations. The approach is simulation-based _~t> use of ~vlarkov chain Monte Carlo techniques. A yletropolis-Hastings i:U~UnLlllll 1::; combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes are derived and compared. The approach is fully Bayesian in obtaining posterior samples for state parameters and unknown hyperparameters. Illustrations to real data sets with sparse counts and missing values are presented. Extensions to accommodate for general distributions for observations and disturbances. intervention. non-linear models and rnultivariate time series are outlined.

Simulation-based smoothing and filtering in factor stochastic volatility models : two econometric applications

In this article we use factor models to describe a certain class of covariance structure for financiaI time series models. More specifical1y, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. We build on previous work by allowing the factor loadings, in the factor mo deI structure, to have a time-varying structure and to capture changes in asset weights over time motivated by applications with multi pIe time series of daily exchange rates. We explore and discuss potential extensions to the models exposed here in the prediction area. This discussion leads to open issues on real time implementation and natural model comparisons.

Simulation -based smoothing and filtering in factor stochastic volatility models : two econometric applications (July-2001)

The past decade has wítenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events aI,"e country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions. In this article we measure the transmission of shocks by cross-market correlation\ coefficients following Forbes and Rigobon's (2000) notion of shift-contagion,. Our main contribution relies upon the use of traditional factor model techniques combined with stochastic volatility mo deIs to study the dependence among Latin American stock price indexes and the North American indexo More specifically, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. From a theoretical perspective, we improve currently available methodology by allowing the factor loadings, in the factor model structure, to have a time-varying structure and to capture changes in the series' weights over time. By doing this, we believe that changes and interventions experienced by those five countries are well accommodated by our models which learns and adapts reasonably fast to those economic and idiosyncratic shocks. We empirically show that the time varying covariance structure can be modeled by one or two common factors and that some sort of contagion is present in most of the series' covariances during periods of economical instability, or crisis. Open issues on real time implementation and natural model comparisons are thoroughly discussed.