Terence C. Mills and Kerry Patterson xvevaluation (Giacomini and White, 2006), evaluating quantile forecasts, and relax-
ing the forecast loss function away from the traditional symmetric squared error.
In short, this chapter provides a clear, critical and accessible evaluation of a rapidly
developing area of the econometrics literature.
Chapter 5 is by Stephen Hall and James Mitchell, who focus on density forecast-
ing. There has been a great deal of policy interest in forecasting key macroeconomic
variables such as output growth and inflation, some of which has been institution-
ally enshrined by granting central banks independence in inflation targeting. In
turn, there has been a movement away from simply reporting point forecasts of
inflation and GDP growth in favor of a fan chart representation of the distribution
of forecasts. A density forecast gives much more information than a simple point
forecast, which is included as just one realization on the outcome axis. As a corol-
lary, forecast evaluation should also include techniques that evaluate the accuracy,
in some well-defined sense, of the density forecast. However, given that generally
we will only be able to observe one outcome (or event) per period, some thought
needs to be given to how the distributional aspect of the forecast is evaluated. Hall
and Mitchell discuss a number of possibilities and also consider methods of eval-
uating competing density forecasts. A further aspect of density forecasting is the
ability of the underlying model to generate time variation in the forecast densi-
ties. If the underlying model is a VAR, or can be approximated by a VAR, then,
subject to some qualifications, the only aspect of the forecast density which is able
to exhibit time variation is the mean; consequently, models have been developed
that allow more general time variation in the density through, for example, ARCH
and GARCH errors and time-varying parameters. This chapter also links in with the
previous chapter by considering combinations of density forecasts. There are two
central possibilities: the linear opinion pool is a weighted linear combination of
the component densities, whereas the logarithmic opinion pool is a multiplicative
combination. Hall and Mitchell consider the problem of determining the weights
in such combinations and suggest that predictive accuracy improves when the
weights reflect shifts in volatility, a characteristic of note for the last decade or so
in a number of economies.
Part III contains four chapters under the general heading of “Time Series Appli-
cations.” A key area in which the concept of a time series is relevant is in
characterizing and determining trends and cycles. Chapter 6, by Stephen Pollock,
is a tour de force on modeling trends and cycles, and on the possibilities and
pitfalls inherent in the different approaches. In the simplest of models, cyclical
fluctuations are purely sinusoidal and the trend is exponential; although simple,
this is a good base from which to understand the nature of developments that
relax these specifications. Such developments include the view that economic time
series evolve through the accumulation of stochastic shocks, as in an integrated
Weiner process. The special and familiar cases of the Beveridge–Nelson decompo-
sition, the Hodrick–Prescott filter, the Butterworth filter and the unifying place of
Weiner–Kolgomorov filtering are all covered with admirable clarity. Other consid-
erations include the complications caused by the limited data that is often available
in economic applications, contrary to the convenient assumptions of theory. In an