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)

Forecast combinations have frequently been found in empirical studies to produce better forecasts on average than methods based on the ex-ante best individual forecasting model. Moreover, simple combinations that ignore correlations between forecast errors often dominate more refined combination schemes aimed at estimating the theoretically optimal combination weights. In this chapter we analyze theoretically the factors that determine the advantages from combining forecasts (for example, the degree of correlation between forecast errors and the relative size of the individual models’ forecast error variances). Although the reasons for the success of simple combination schemes are poorly understood, we discuss several possibilities related to model misspecification, instability (non-stationarities) and estimation error in situations where thenumbersofmodelsislargerelativetothe available sample size. We discuss the role of combinations under asymmetric loss and consider combinations of point, interval and probability forecasts. Key words: Forecast combinations; pooling and trimming; shrinkage methods; model misspecification, diversification gains

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

combining the forecasts in the ecb survey of professional forecasters can anything beat the simple average? by Véronique Genre,

: Most of the literature on combination of forecasts deals with the assumption of unbiased individual forecasts. Here, we consider the case of biased forecasts and discuss two different combination techniques resulting in an unbiased forecast. On the one hand we correct the individual forecasts, and on the other we calculate bias based weights. A simulation study gives some insight in the situations where we should use the different methods. Key words: combination of forecasts, bias correction, regression, generalized Jackknife, multivariate forecasts. Acknowledgement: Financial support of the Deutsche Forschungsgemeinschaft (SFB 475, "Reduction of complexity in multivariate data structures") is gratefully acknowledged. AMS 1991 Subject classification: 62F10 2 1. Introduction The combination of forecasts is usually based on the assumption of unbiased individual forecasts. In the univariate case we restrict the combination weights to sum up to one which results also in an unbiased f...

The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada. iii

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. The paper proposes an algorithm that uses forecast encompassing tests for combining forecasts. The algorithm excludes a forecast from the combination if it is encompassed by another forecast. To assess the usefulness of this approach, an extensive empirical analysis is undertaken using a U.S. macroecoomic data set. The results are encouraging as the algorithm forecasts outperform benchmark model forecasts, in a mean square error (MSE) sense, in a majority of cases.

with several members of the “Economic Analysis and Forecasting Department ” at the Banco de España. We would also like to thank, without implicating, Samuel Hurtado, Gabriel Perez-Quiros and Alberto Urtasun for comments and suggestions at the earliest stage of the work. DISCLAIMER: The views expressed in this paper are the author’s, not those of Banco de España. Documentos de Trabajo. N.º 1037 2010 The Working Paper Series seeks to disseminate original research in economics and fi nance. All papers have been anonymously refereed. By publishing these papers, the Banco de España aims to contribute to economic analysis and, in particular, to knowledge of the Spanish economy and its international environment. The opinions and analyses in the Working Paper Series are the responsibility of the authors and, therefore, do not necessarily coincide with those of the Banco de España or the Eurosystem. The Banco de España disseminates its main reports and most of its publications via the INTERNET at the following website:

This paper undertakes a Bayesian analysis of optimal monetary policy for the U.K. We estimate a suite of monetary-policy models that include both forwardand backward-looking representations as well as large- and small-scale models. We find an optimal simple Taylor-type rule that accounts for both model and parameter uncertainty. For the most part, backward-looking models are highly fault tolerant with respect to policies optimized for forward-looking representations, while forward-looking models have low fault tolerance with respect to policies optimized for backward-looking representations. In addition, backward-looking models often have lower posterior probabilities than forwardlooking models. Bayesian policies therefore have characteristics suitable for inflation and output stabilization in forward-looking models. 1

Combining expert forecasts: Can anything beat the simple average? 1