This book provides a formal analysis of the models, procedures, and measures of economic forecasting with a view to improving forecasting practice. David Hendry and Michael Clements base the analyses on assumptions pertinent to the economies to be forecast, viz. a non-constant, evolving economic system, and econometric models whose form and structure are unknown a priori. The authors find that conclusions which can be established formally for constant-parameter stationary processes and correctly-specified models often do not hold when unrealistic assumptions are relaxed. Despite the difficulty of proceeding formally when models are mis-specified in unknown ways for non-stationary processes that are subject to structural breaks, Hendry and Clements show that significant insights can be gleaned. For example, a formal taxonomy of forecasting errors can be developed, the role of causal information clarified, intercept corrections re-established as a method for achieving robustness against forms of structural change, and measures of forecast accuracy re-interpreted.

We consider forecasting using a combination, when no model coincides with a non-constant data generation process (DGP). Practical experience suggests that combining forecasts adds value, and can even dominate the best individual device. We show why this can occur when forecasting models are differentially mis-specified, and is likely to occur when the DGP is subject to location shifts. Moreover, averaging may then dominate over estimated weights in the combination. Finally, it cannot be proved that only non-encompassed devices should be retained in the combination. Empirical and Monte Carlo illustrations confirm the analysis.solutions to forecast biases and inefficiencies than pooling forecasts. Moreover, it is less easy to see why a combination need improve over the best of a group, particularly if there are some decidedly poor forecasts in that group.Second, in non-stationary time series, most forecasts will fail in the same direction when forecasting over a period within which a break unexpectedly occurs. Combination is unlikely to provide a substantial improvement over the best individual forecasts in such a setting. Nevertheless, what will occur when forecasting after a location shift depends on the extent of model misspecifications, data correlations, the sizes of breaks and so on, so combination might help. Since a theory of forecasting allowing for model mis-specification interacting with intermittent location shifts has explained many other features of the empirical forecasting literature (see Clements and Hendry 1999), we explore the possibility that it can also account for the benefits from pooling.Third, averaging reduces variance to the extent that separate sources of information are used. Since we allow all models to be differentially mis-specified, such variance reduction remains possible. Nevertheless, we will ignore sample estimation uncertainty to focus on specification issues, so any gains from averaging also reducing that source of variance will be additional to those we delineate. 1 Next, an alternative interpretation of combination is that, relative to a 'baseline' forecast, additional forecasts act like intercept corrections (ICs). It is well known that appropriate ICs can improve forecasting performance not only if there are structural breaks, but also if there are deterministic mis-specifications. Indeed, Clements and Hendry (1999) present eight distinct interpretations of the role that ICs can play in forecasting, and for example, interpret the crosscountry pooling in Hoogstrate et al. (2000) as a specific form of IC.Finally, pooling can also be viewed as an application of the Stein-James 'shrinkage' estimation (see e.g. Judge and Bock 1978). If the unknown future value is viewed as a 'meta-parameter' of which all the individual forecasts are estimates, then averaging may provide a 'better' estimate thereof. Below, we consider whether data-based weighting will be useful when the process is subject to unanticipated breaks. Thus, we evaluate the possible benefits of combining forecasts i...

Linear models are invariant under non-singular, scale-preserving linear transformations, whereas mean square forecast errors (MSFEs) are not. Different rankings may result across models or methods from choosing alternative yet isomorphic representations of a process. One approach can dominate others for comparisons in levels, yet lose to another for differences, to a second for cointegrating vectors and to a third for combinations of variables. The potential for switches in ranking is related to criticisms of the inadequacy of MSFE against encompassing criteria, which are invariant under linear transforms and entail MSFE dominance. An invariant evaluation criterion which avoids misleading outcomes is examined in a Monte Carlo study of forecasting methods.

Although many macroeconomic series such as US real output growth are sampled quarterly, many potentially useful predictors are observed at a higher frequency. We look at whether a recently developed mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth and inflation. We carry out a number of related real-time forecast comparisons using various indicators as explanatory variables. We find that MIDAS model forecasts of output growth are more accurate at horizons less than one quarter using coincident indicators; that MIDAS models are an effective way of combining information from multiple indicators;and that the forecast accuracy of the unemployment-rate Phillips curve for inflation is enhanced using the MIDAS approach.Keywords: Data frequency, multiple predictors, combination, real-time forecasting.JEL classification: C51, C53. * We are grateful to the Editor, an Associate Editor, and two anonymous referees for helpful comments and guidance. We also acknowledge helpful comments from participants at the International Symposium of Forecasting Macroeconomic Forecasting with Mixed Frequency Data:Forecasting US output growth and inflation AbstractAlthough many macroeconomic series such as US real output growth are sampled quarterly, many potentially useful predictors are observed at a higher frequency. We look at whether a recently developed mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth and inflation. We carry out a number of related real-time forecast comparisons using various indicators as explanatory variables. We find that MIDAS model forecasts of output growth are more accurate at horizons less than one quarter using coincident indicators; that MIDAS models are an effective way of combining information from multiple indicators; and that the forecast accuracy of the unemployment-rate Phillips curve for inflation is enhanced using the MIDAS approach.