200 Recent Developments in Density Forecasting
5.1 Introduction
Forecasts of the future values of economic variables are used widely in decision
making. For example, in many countries inflation forecasts are now central to
the setting of monetary policy since monetary policy works with a lag (e.g., see
Svensson, 2005, for a review). But it has become increasingly well understood
that it is not a question of this forecast proving to be “right” and that forecast
proving to be “wrong.” Point forecasts, the traditional focus, are better seen as
the central points of ranges of uncertainty. A forecast of, say, 2% must mean that
people should not be surprised if actual inflation turns out to be a little larger
or smaller than that. Moreover, at a time of heightened economic uncertainty,
they should not be very surprised if it turns out to be much larger or smaller.
Consequently, to provide a complete description of the uncertainty associated with
the point forecast many professional forecasters now publish density forecasts, or
more popularly “fan charts.” A famous example is the Bank of England’s fan chart
(see Britton, Fisher and Whitley, 1998). Importantly, as this chapter reviews, just
as point forecasts are commonly evaluated using the subsequent outturn, so the
reliability of uncertainty forecasts can be evaluated.
More formally, density forecasts of inflation provide an estimate of the prob-
ability distribution of its possible future values. In contrast to interval forecasts,
which give the probability that the outcome will fall within a stated interval, such
as inflation falling within its target range, density forecasts provide a complete
description of the uncertainty associated with a forecast; they can thus be seen to
provide information on all possible intervals.
In conjunction with the increased use of density forecasts by professional fore-
casters and central banks, the academic literature has also devoted increased
emphasis to density forecasting, with theJournal of Forecastingdevoting a spe-
cial issue to it in 2000 and theHandbook of Economic Forecasting, published in
2006, containing a chapter surveying methods for predictive density evaluation.
This chapter, with a macroeconomic focus, reviews several aspects of these recent
developments, breaking them down into four areas which, in turn, are considered
in separate sections of the chapter:
- The importance of density forecasts
- The production of density forecasts
- The evaluation of density forecasts
- The combination of density forecasts.
In so doing we extend the coverage, and update in the light of recent research,
previous surveys and textbooks, including Tay and Wallis (2000), Clements (2005),
Timmermann (2006) and Wallis (2008). The principal extensions in terms of
coverage are the last two sections. In particular we focus on how to choose the
weights when combining density forecasts. Reflecting the infancy of this material,
considerable applied and theoretical work remains to be done to establish a con-
sensus about how best this should be achieved. Nevertheless, this chapter attempts