Conditional predictive density evaluation in the presence of instabilities

We propose new methods for evaluating predictive densities. The methods includeKolmogorov-Smirnov and Cram?r-von Mises-type tests for the correct specification ofpredictive densities robust to dynamic mis-specification. The novelty is that the testscan detect mis-specification in the predictive densities even if it appears only overa fraction of the sample, due to the presence of instabilities. Our results indicatethat our tests are well sized and have good power in detecting mis-specification inpredictive densities, even when it is time-varying. An application to density forecastsof the Survey of Professional Forecasters demonstrates the usefulness of the proposedmethodologies.

Out-of-sample forecast tests robust to the choice of window size

This paper proposes new methodologies for evaluating out-of-sample forecastingperformance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide rangeof window sizes. We show that the tests proposed in the literature may lack the powerto detect predictive ability and might be subject to data snooping across differentwindow sizes if used repeatedly. An empirical application shows the usefulness of themethodologies for evaluating exchange rate models' forecasting ability.

Combining multivariate density forecasts using predictive criteria

This paper combines multivariate density forecasts of output growth, inflationand interest rates from a suite of models. An out-of-sample weighting scheme based onthe predictive likelihood as proposed by Eklund and Karlsson (2005) and Andersson andKarlsson (2007) is used to combine the models. Three classes of models are considered: aBayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR)and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australiandata, we find that, at short forecast horizons, the Bayesian VAR model is assignedthe most weight, while at intermediate and longer horizons the factor model is preferred.The DSGE model is assigned little weight at all horizons, a result that can be attributedto the DSGE model producing density forecasts that are very wide when compared withthe actual distribution of observations. While a density forecast evaluation exercise revealslittle formal evidence that the optimally combined densities are superior to those from thebest-performing individual model, or a simple equal-weighting scheme, this may be a resultof the short sample available.

Exchange rate predictability

The main goal of this article is to provide an answer to the question: "Does anything forecast exchange rates, and if so, which variables?". It is well known thatexchange rate fluctuations are very difficult to predict using economic models, andthat a random walk forecasts exchange rates better than any economic model (theMeese and Rogoff puzzle). However, the recent literature has identified a series of fundamentals/methodologies that claim to have resolved the puzzle. This article providesa critical review of the recent literature on exchange rate forecasting and illustratesthe new methodologies and fundamentals that have been recently proposed in an up-to-date, thorough empirical analysis. Overall, our analysis of the literature and thedata suggests that the answer to the question: "Are exchange rates predictable?" is,"It depends" -on the choice of predictor, forecast horizon, sample period, model, andforecast evaluation method. Predictability is most apparent when one or more of thefollowing hold: the predictors are Taylor rule or net foreign assets, the model is linear, and a small number of parameters are estimated. The toughest benchmark is therandom walk without drift.

Alternative tests for correct specification of conditional predictive densities

We propose new methods for evaluating predictive densities that focus on the models' actual predictive ability in finite samples. The tests offer a simple way of evaluatingthe correct specification of predictive densities, either parametric or non-parametric.The results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities. An empirical application to the Survey ofProfessional Forecasters and a baseline Dynamic Stochastic General Equilibrium modelshows the usefulness of our methodology.