In this paper we investigate whether and how far density forecasts sensibly can be combined to produce a “better ” pooled density forecast. In so doing we bring together two important but hitherto largely unrelated areas of the forecasting literature in economics, density forecasting and forecast combination. We provide simple Bayesian methods of pooling information across alternative density forecasts. We illustrate the proposed techniques in an application to two widely used published density forecasts for U.K. inflation. We examine whether in practice improved density forecasts for inflation, one year ahead, might have been obtained if one had combined the Bank of England and NIESR density forecasts or “fan charts”. 1

This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as ‘average ’ models. The asymptotic as well as the exact finite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991-2007. The empirical evidence supports the use of ‘thick’ model averaging strategies over single models or Bayesian type model averaging procedures.

This paper attempts to provide a conceptual framework for the analysis of counterfactual scenarios using macroeconometric models. As an application we consider UK entry to the euro. Entry involves a long-term commitment to restrict UK nominal exchange rates and interest rates to be the same as those of the euro area. We derive conditional probability distributions for the difference between the future realisations of variables of interest (e.g UK and euro area output and prices) subject to UK entry restrictions being fully met over a given period and the alternative realisations without the restrictions. The robustness of the results can be evaluated by also conditioning on variables deemed to be invariant to UK entry, such as oil or US equity prices. Economic interdependence means that such policy evaluation must take account of international linkages and common factors that drive fluctuations across economies. In this paper this is accomplished using the Global VAR recently developed by Dees, di Mauro, Pesaran and Smith (2005). The paper briefly describes the GVAR which has been estimated for 25 countries and the euro area over the period 1979-2003. It reports probability estimates that output will be higher and prices lower in the UK and the euro area as a result of entry. It examines the sensitivity of these results to a variety of assumptions about when and how the UK entered and the observed global shocks and compares them with the effects of Swedish entry.

This paper attempts to provide a conceptual framework for the analysis of counterfactual scenarios using macroeconometric models. As an application we consider UK entry to the euro. Entry involves a long-term commitment to restrict UK nominal exchange rates and interest rates to be the same as those of the euro area. We derive conditional probability distributions for the difference between the future realisations of variables of interest (e.g UK and euro area output and prices) subject to UK entry restrictions being fully met over a given period and the alternative realisations without the restrictions. The robustness of the results can be evaluated by also conditioning on variables deemed to be invariant to UK entry, such as oil or US equity prices. Economic interdependence means that such policy evaluation must take account of international linkages and common factors that drive fluctuations across economies. In this paper this is accomplished using the Global VAR recently developed by Dees, di Mauro, Pesaran and Smith (2006). The paper briefly describes the GVAR which has been estimated for 25 countries and the euro area over the period 1979-2003. It reports probability estimates that output will be higher and prices lower in the UK and the euro area as a result of entry. It examines the sensitivity of these results to a variety of assumptions about when and how the UK entered and the observed global shocks and compares them with the effects of Swedish entry.

This paper uses vector error correction models of Switzerland for forecasting output, inflation and the short-term interest rate. It considers three different ways of dealing with forecast uncertainties. First, it investigates the effect on forecasting performance of averaging over forecasts from different models. Second, it considers averaging forecasts from different estimation windows. It is found that averaging over estimation windows is at least as effective as averaging over different models and both complement each other. Third, it examines whether using weighting schemes from the machine learning literature improves the average forecast. Compared to equal weights the effect of alternative weighting schemes on forecast accuracy is small in the present application. JEL classification: C53, C32

Abstract not found

We develop a theoretical model to compare forecast uncertainty estimated from time series models to those available from survey density forecasts. The sum of the average variance of individual densities and the disagreement is shown to approximate the predictive uncertainty from well-specified time series models when the variance of the aggregate shocks is relatively small compared to that of the idiosyncratic shocks. Due to grouping error problems and compositional heterogeneity in the panel, individual densities are used to estimate aggregate forecast uncertainty. During periods of regime change and structural break, ARCH estimates tend to diverge from survey measures.

We develop an unobserved components approach to study surveys of forecasts containing multiple forecast horizons. Under the assumption that forecasters optimally update their beliefs about past, current and future state variables as new information arrives, we use our model to extract information on the degree of predictability of the state variable and the importance of measurement errors in the observables. Empirical estimates of the model are obtained using survey forecasts of annual GDP growth and in‡ation in the US with forecast horizons ranging from 1 to 24 months, and the model is found to closely match the joint realization of forecast errors at di¤erent horizons. Our empirical results suggest that professional forecasters face severe measurement error problems for GDP growth in real time, while this is much less of a problem for in‡ation. Moreover, in-‡ation exhibits greater persistence, and thus is predictable at longer horizons, than GDP growth and the persistent component of both variables is well-approximated by a low-order autoregressive speci…cation. Keywords: Fixed-event forecasts, multiple forecast horizons, Kalman …ltering, survey data. *We thank the editor, Serena Ng, an associate editor and two anonymous referees for constructive comments.

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledged and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treat-ment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks of forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of “real time econometrics”. This paper attempts to provide an overview of some of these developments.

This article describes the use of Bayesian methods in the statistical analysis of time series. The use of Markov chain Monte Carlo methods has made even the more complex time series models amenable to Bayesian analysis. Models discussed in some detail are ARIMA models and their fractionally integrated counterparts, state-space models, Markov switching and mixture models, and models allowing for time-varying volatility. A final section reviews some recent approaches to nonparametric Bayesian modelling of time series.