Stephen G. Hall and James Mitchell 203but equals:
̂yt|t−h=E(yt|t−h)+
φV(yt|t−h)
2
, (5.1)whereφis the asymmetry parameter in the Linex function. It reflects differing costs
to over and under prediction. This means that it can be “rational” for the user to
focus on what are effectively biased point (conditional mean) forecasts.
The trend towards forecasters publishing density forecasts is also explained by the
obvious advantages they bring when communicating with the public and remind-
ing them that the forecasters themselves expect the point forecasts to be “wrong.”
Indeed, interest may lie in the dispersion or tails of the density itself; e.g., infla-
tion targets often focus the attention of monetary authorities to the probability of
future inflation falling within some predefined target range, while users of growth
forecasts may be concerned about the probability of recession. These probability
event forecasts can readily be extracted from the density forecast. In addition,
ranking forecasting models according to their point forecasting performance alone
can be misleading. For example, Clementset al.(2003) find that the failure to
find empirical support out-of-sample for nonlinear business cycle forecasts may be
explained by the traditional focus on point forecasts and their root mean squared
error (RMSE). They argue that nonlinear models may do better at forecasting the
higher moments that are captured by density forecasts.
5.3 The production of density forecasts
In general, forecasts can be produced in a wide variety of ways, ranging from com-
plete model-based approaches to pure judgmental approaches, sometimes referred
to as Delphic forecasts; indeed, almost any combination of model and judgment is
possible. In the conventional point forecasting world, it is probably fair to say that
almost all forecasts which are made by policy or commercial institutes involve
a considerable degree of judgment, although there is, of course, a considerable
academic literature on pure model-based forecasts. When we consider density fore-
casting, a similar range of formal and informal techniques are used, although it is
probably fair to say that, given the greater complexity of a density forecast, there
should be more reliance on formal model-based information.
There is not a widespread, long history of regular published density forecasts in
macroeconomics. One of the longest continuously published series is the Survey
of Professional Forecasters (SPF), which is now conducted by the Federal Reserve
Bank of Philadelphia and was originally started in 1968 by the American Statistical
Association and the National Bureau of Economic Research.
Nevertheless, there is a tradition, which has been maintained to the present day,
of publishing (unbalanced) panel data sets of competing point forecasts. For exam-
ple, in the UK each month since January 1987 Her Majesty’s Treasury (HMT) has
collected together, in its publicationForecasts for the UK Economy: A Comparison
of Independent Forecasts, the point forecasts of (as of December 2007) 43 indepen-
dent City and non-City forecasters. Disagreement among forecasters (as measured
by the variance of competing point forecasts at a given point in time) has then