It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

this paper we first illustrate the above considerations for a variety of appealling criteria, and then, in an attempt to understand this behaviour, introduce a new game-theoretic framework for Probability Theory, the `prequential framework', which is particularly suited for the study of such problems.

Statistical loss functions that generally lack economic content are commonly used for evaluating financial volatility forecasts. In this paper, an evaluation framework based on loss functions tailored to a user’s economic interests is proposed. According to these interests, the user specifies the economic events to be forecast, the criterion with which to evaluate these forecasts, and the subsets of the forecasts of particular interest. The volatility forecasts from a model are then transformed into probability forecasts of the relevant events and evaluated using the specified criteria (i.e., a probability scoring rule and calibration tests). An empirical example using exchange rate data illustrates the framework and confirms that the choice of loss function directly affects the forecast evaluation results.

Projections of future climate change caused by increasing greenhouse gases depend critically on numerical climate models coupling the ocean and atmosphere (GCMs). However, different models differ substantially in their projections, which raises the question of how the different models can best be combined into a probability distribution of future climate change. For this analysis, we have collected both current and future projected mean temperatures produced by nine climate models for 22 regions of the earth. We also have estimates of current mean temperatures from actual observations, together with standard errors, that can be used to calibrate the climate models. We propose a Bayesian analysis that allows us to combine the different climate models into a posterior distribution of future temperature increase, for each of the 22 regions, while allowing for the different climate models to have different variances. Two versions of the analysis are proposed, a univariate analysis in which each region is analyzed separately, and a multivariate analysis in which the 22 regions are combined into an overall statistical model. A cross-validation approach is proposed to confirm the reasonableness of our Bayesian predictive distributions. The results of this analysis allow for a quantification of the uncertainty of climate model projections as a Bayesian posterior distribution, substantially extending previous approaches to uncertainty in climate models.

SUMMARY. Here we give a technique for online prediction that uses different model selection principles (MSP’s) at different times. The central idea is that each MSP is associated with a collection of models for which it is best suited. This means one can use the data to choose an MSP. Then, the MSP chosen is used with the data to choose a model, and the parameters of the model are estimated so that predictions can be made. Depending on the degree of discrepancy between the predicted values and the actual outcomes one may update the parameters within a model, re-use the MSP to rechoose the model and estimate its parameters, or start all over again rechoosing the MSP. Our main formal result is a theorem which gives conditions under which our technique performs better than always using the same MSP. We also discuss circumstances under which dropping data points may lead to better predictions. 1.

this paper have implicity assumed a single homogeneous sample. However, they are also applicable in multi-sample problems, in which the parameters of the model are possibly different from one sample to another. Such problems lead to what are usually called empirical Bayes methods of analysis. In recent years it has become more common to solve such problems from a fully Bayesian point of view, using a hierarchical model structure to link together the parameters of the different subsamples. This is the point of view taken, for example, in the excellent recent monograph by Carlin and Louis (1996). Despite the very rapid growth of this field, there has been comparatively little study of the frequentist properties of Bayesian procedures in this setting. Berger and Strawderman (1996) established some admissibility results, which have the advantage of not relying on any kind of asymptotics, and which provide guidance on the choice of prior particularly where improper priors are concerned. On the other hand, the class of models to which their results apply is restrictive, and admissibility results do not necessarily help to pick out a prior distribution which has good properties under particular conditions. In contrast, the results of the present paper are asymptotic (letting sample size n !1 while the number of samples remains fixed) but they do allow explicit computations to be made under a veriety of circumstances. In the present section, these ideas are worked out in some detail for the simplest problem in this class: the case of p normal distributions with unknown means and known common variance. In the next section, a more complicated example is considered. Suppose there are p subgroups and the data in the j'th subgroup follow a N(` j ; 1) distribution. Here the vector ...

this paper in Valencia.

Artificial intelligence has its roots in symbolic logic, and for many years it showed little interest in probability. But during the past decade, disinterest has been replaced by engagement. The flowering of expert systems during the 1980s strengthened ties between AI and areas of engineering and business that had long used probability and led to hybrid rule-based and probabilistic expert systems for a plethora of engineering and business problems, including speech recognition, vision, site selection, and process control. At the same time, probabilistic and statistical thinking has penetrated many areas of AI theory, including learning (Vapnik 1983, Valiant 1991), planning (Dean and Wellman 1991), and the evaluation of 1 artificial agents (Cohen 1990), to the point that AI has emerged as a contributor to the theory of probability and statistics. What can the new role for probability in AI teach us about the philosophy of probability? Do the old interpretations of probability do

this paper, however, shows that this is too simple a conclusion. For many models, when assessed

We investigate the importance of the assumed covariance structure for longitudinal modelling of CD4 counts. We examine how individual predictions of future CD4 counts are affected by the covariance structure. We consider four covariance structures: one based on an integrated Ornstein-Uhlenbeck stochastic process, one based on Brownian motion and two derived from standard linear and quadratic random e#ects models. Using data from the Multicenter AIDS Cohort Study and from a simulation study,we show that there is a noticeable deterioration in the coverage rate of confidence intervals if we assume the wrong covariance. There is also a loss in e#ciency. The quadratic random effects model is found to be the best in terms of correctly calibrated prediction intervals, but is substantially less efficient than the others. Incorrectly specifying the covariance structure as linear random effects gives too narrow prediction intervals with poor coverage rates. Fitting using the model based on th...