Forecasting in dynamic factor models using Bayesian model averaging

This paper considers the problem of forecasting in dynamic factor models using Bayesian model averaging. Theoretical justifications for averaging across models, as opposed to selecting a single model, are given. Practical methods for implementing Bayesian model averaging with factor models are described. These methods involve algorithms which simulate from the space defined by all possible models. We discuss how these simulation algorithms can also be used to select the model with the highest marginal likelihood (or highest value of an information criterion) in an efficient manner. We apply these methods to the problem of forecasting GDP and inflation using quarterly U.S. data on 162 time series. For both GDP and inflation, we find that the models which contain factors do out-forecast an AR(p), but only by a relatively small amount and only at short horizons. We attribute these findings to the presence of structural instability and the fact that lags of dependent variable seem to contain most of the information relevant for forecasting. Relative to the small forecasting gains provided by including factors, the gains provided by using Bayesian model averaging over forecasting methods based on a single model are appreciable

Reconsidering the role of monetary indicators for euro area inflation from a Bayesian perspective using group inclusion probabilities

This paper addresses the relative importance of monetary indicators for forecasting inflation in the euro area in a Bayesian framework. Bayesian Model Averaging (BMA)based on predictive likelihoods provides a framework that allows for the estimation of inclusion probabilities of a particular variable, that is the probability of that variable being in the forecast model. A novel aspect of the paper is the discussion of group-wise inclusion probabilities, which helps to address the empirical question whether the group of monetary variables is relevant for forecasting euro area inflation. In our application, we consider about thirty monetary and non-monetary indicators for inflation. Using this data, BMA provides inclusion probabilities and weights for Bayesian forecast combination. The empirical results for euro area data show that monetary aggregates and non-monetary indicators together play an important role for forecasting inflation, whereas the isolated information content of both groups is limited. Forecast combination can only partly outperform single-indicator benchmark models. --inflation forecasting,monetary indicators,Bayesian Model Averaging,inclusion probability

Universality of Bayesian Predictions

Given the sequential update nature of Bayes rule, Bayesian methods find natural application to prediction problems. Advances in computational methods allow to routinely use Bayesian methods in econometrics. Hence, there is a strong case for feasible predictions in a Bayesian framework. This paper studies the theoretical properties of Bayesian predictions and shows that under minimal conditions we can derive finite sample bounds for the loss incurred using Bayesian predictions under the Kullback-Leibler divergence. In particular, the concept of universality of predictions is discussed and universality is established for Bayesian predictions in a variety of settings. These include predictions under almost arbitrary loss functions, model averaging, predictions in a non stationary environment and under model miss-specification. Given the possibility of regime switches and multiple breaks in economic series, as well as the need to choose among different forecasting models, which may inevitably be miss-specified, the finite sample results derived here are of interest to economic and financial forecasting

Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information

We forecast the term structure of U.S. Treasury zero-coupon bond yields by analyzing a range of models that have been used in the literature. We assess the relevance of parameter uncertainty by examining the added value of using Bayesian inference compared to frequentist estimation techniques, and model uncertainty by combining forecasts from individual models. Following current literature we also investigate the benefits of incorporating macroeconomic information in yield curve models. Our results show that adding macroeconomic factors is very beneficial for improving the out-of-sample forecasting performance of individual models. Despite this, the predictive accuracy of models varies over time considerably, irrespective of using the Bayesian or frequentist approach. We show that mitigating model uncertainty by combining forecasts leads to substantial gains in forecasting performance, especially when applying Bayesian model averaging

Improving forecasting performance using covariate-dependent copula models

Copulas provide an attractive approach for constructing multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of explicitly forecasting the tail-dependences. Most of the available approaches are only able to estimate tail-dependences and correlations via nuisance parameters, but can neither be used for interpretation, nor for forecasting. Aiming to improve copula forecasting performance, we propose a general Bayesian approach for modeling and forecasting tail-dependences and correlations as explicit functions of covariates. The proposed covariate-dependent copula model also allows for Bayesian variable selection among covariates from the marginal models as well as the copula density. The copulas we study include Joe-Clayton copula, Clayton copula, Gumbel copula and Student's \emph{t}-copula. Posterior inference is carried out using an efficient MCMC simulation method. Our approach is applied to both simulated data and the S\&P 100 and S\&P 600 stock indices. The forecasting performance of the proposed approach is compared with other modeling strategies based on log predictive scores. Value-at-Risk evaluation is also preformed for model comparisons

Comment on `Tainted evidence: cosmological model selection versus fitting', by Eric V. Linder and Ramon Miquel (astro-ph/0702542v2)

In astro-ph/0702542v2, Linder and Miquel seek to criticize the use of Bayesian model selection for data analysis and for survey forecasting and design. Their discussion is based on three serious misunderstandings of the conceptual underpinnings and application of model-level Bayesian inference, which invalidate all their main conclusions. Their paper includes numerous further inaccuracies, including an erroneous calculation of the Bayesian Information Criterion. Here we seek to set the record straight.Comment: 6 pages RevTeX

What do Bayesian methods offer population forecasters?

The Bayesian approach has a number of attractive properties for probabilistic forecasting. In this paper, we apply Bayesian time series models to obtain future population estimates with uncertainty for England and Wales. To account for heterogeneity found in the historical data, we add parameters to represent the stochastic volatility in the error terms. Uncertainty in model choice is incorporated through Bayesian model averaging techniques. The resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using traditional stochastic models. Firstly, data and uncertainties in the parameters and model choice are explicitly included using probability distributions. As a result, more realistic probabilistic population forecasts can be obtained. Second, Bayesian models formally allow the incorporation of expert opinion, including uncertainty, into the forecast. Our results are discussed in relation to classical time series methods and existing cohort component projections. This paper demonstrates the flexibility of the Bayesian approach to simple population forecasting and provides insights into further developments of more complicated population models that include, for example, components of demographic change

Forecasting Large Datasets with Reduced Rank Multivariate Models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance with the most promising existing alternatives, namely, factor models, large scale bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two-step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank bayesian VAR of Geweke (1996). As a result, we found that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast, and for key variables such as industrial production growth, inflation, and the federal funds rate.Bayesian VARs, Factor models, Forecasting, Reduced rank