A generalized predictive criterion for model selection

Given a random sample from some unknown model belonging to a finite class of parametric models, assume that the estimate of the density of a future observation is of interest San Martini & Spezzaferri (1984) proposed for this problem a predictive criterion based on the logarithmic utility function. The present authors investigate a generalization of this criterion that uses as a loss function an element of the class of α‐divergences discussed by Ali & Silvey (1966) and Csiszár (1967). They also discuss briefly the case in which the class of models considered is not exhaustive.     

Bayes factors for goodness of fit testing

We propose the use of the generalized fractional Bayes factor for testing fit in multinomial models. This is a non-asymptotic method that can be used to quantify the evidence for or against a sub-model. We give expressions for the generalized fractional Bayes factor and we study its properties. In particular, we show that the generalized fractional Bayes factor has better properties than the fractional Bayes factor.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Event-tree analysis with imprecise probabilities

Novel methods are proposed for dealing with event-tree analysis under imprecise probabilities, where one could measure chance or uncertainty without sharp numerical probabilities and express available evidence as upper and lower previsions (or expectations) of gambles (or bounded real functions). Sets of upper and lower previsions generate a convex set of probability distributions (or measures). Any probability distribution in this convex set should be considered in the event-tree analysis. This article focuses on the calculation of upper and lower bounds of the prevision (or the probability) of some outcome at the bottom of the event-tree. Three cases of given information/judgments on probabilities of outcomes are considered: (1) probabilities conditional to the occurrence of the event at the upper level; (2) total probabilities of occurrences, that is, not conditional to other events; (3) the combination of the previous two cases. Corresponding algorithms with imprecise probabilities under the three cases are explained and illustrated by simple examples.     

Energy statistics: A class of statistics based on distances

Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. Thus even if the observations are complex objects, like functions, one can use their real valued nonnegative distances for inference. Theory and application of energy statistics are discussed and illustrated. Finally, we explore the notion of potential and kinetic energy of goodness-of-fit.     

Optimal predictive sample size for case–control studies

Summary.  The identification of factors that increase the chances of a certain disease is one of the classical and central issues in epidemiology. In this context, a typical measure of the association between a disease and risk factor is the odds ratio. We deal with design problems that arise for Bayesian inference on the odds ratio in the analysis of case–control studies. We consider sample size determination and allocation criteria for both interval estimation and hypothesis testing. These criteria are then employed to determine the sample size and proportions of units to be assigned to cases and controls for planning a study on the association between the incidence of a non-Hodgkin's lymphoma and exposition to pesticides by eliciting prior information from a previous study.     

Policy strategies for economic development in Cuba: A simulation model analysis

The economic reforms implemented in Cuba since 2008 do not adequately deal with the structural issues that hamper the country's economic development. The article presents a system dynamics model to investigate Cuba's development process, and a simulation analysis to compare different policy scenarios that may be realized in the future as economic reforms will continue. The results indicate that the most effective development policy would be to combine active public policies to enhance the research and development sector on the one hand, and to foster the emergence of an efficient private sector that will develop the capital infrastructure of the economy on the other.     

On the predictive performance of a non-optimal action in hypothesis testing

Statistical Methods & Applications - In Bayesian decision theory, the performance of an action is measured by its posterior expected loss. In some cases it may be convenient/necessary to use a...     

A Stochastic Volatility Model With Realized Measures for Option Pricing

Abstract

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options.     

Bond Risk Premia Forecasting: A Simple Approach for Extracting Macroeconomic Information from a Panel of Indicators

We propose a simple but effective estimation procedure to extract the level and the volatility dynamics of a latent macroeconomic factor from a panel of observable indicators. Our approach is based on a multivariate conditionally heteroskedastic exact factor model that can take into account the heteroskedasticity feature shown by most macroeconomic variables and relies on an iterated Kalman filter procedure. In simulations we show the unbiasedness of the proposed estimator and its superiority to different approaches introduced in the literature. Simulation results are confirmed in applications to real inflation data with the goal of forecasting long-term bond risk premia. Moreover, we find that the extracted level and conditional variance of the latent factor for inflation are strongly related to NBER business cycles.