Pooling of forecasts

Abstract

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...

Forecasting growth and inflation in an enlarged euro area

“…This is due to over-weighting the smaller countries, such as Ireland, Latvia and Lithuania, where forecast performance is the poorest. Hendry and Clements (2004) propose a number of reasons as to why pooled forecasts might out-perform the aggregate. They argue that pooling forecasts from various candidate models allows alternative models to act as 'intercept corrections', which have been shown to improve forecasts in the presence of structural breaks and/or model misspecifi cation.…”

15. Some Policy Implications

“…This is due to over-weighting the smaller countries, such as Ireland, Latvia and Lithuania where forecast performance is poorest. Hendry and Clements (2004) propose a number of reasons as to why pooled forecasts might out-perform the aggregate. They argue that pooling forecasts from various candidate models allows alternative models to act as 'intercept corrections', which have been shown to improve forecasts in the presence of structural breaks and /or model mis-specification.…”

Forecast combination for discrete choice models: predicting FOMC monetary policy decisions

“…Timmermann (2006) provide an extensive survey of the literature and list the advantages one can expect from pooling forecasts. Other useful surveys are provided by Clemen (1989), Diebold and Lopez (1996) and Hendry and Clements (2004).…”