Density forecasting is rapidly becoming a very active and important area of research in the analysis of economic and _nancial time series and this special issue surveys and takes stock of recent developments in the _eld[ The issue begins with a survey article by Tay and Wallis and is followed by seven papers that cover a range of issues related to the estimation and evaluation of density forecasts[
The need to consider the full predictive density of a time series rather than\ say\ its conditional mean or variance has of course long been recognized in a decision!theoretical context[ A decision maker whose loss function depends asymmetrically on the outcome of future values of possibly non!Gaussian variables will generally want to know not only the conditional mean and variance but also the full conditional density of the variables[ The increase in modern computing power has made calculation of density forecasts possible\ if not quite yet a routine exercise\ in the frequently encountered cases where a closed form does not exist for the predictive distribution or where the parameters of this distribution are complicated\ non!linear functions of the data[ Studies of _nancial market data is an area where the payo} from going well beyond modelling the conditional mean in forecasting exercises is particularly clear so it is unsurprising that most applications in this issue apply such data[ Early experiences with _nancial returns showed that their levels\ particularly when measured at high frequencies\ are very di.cult to predict[ This follows in part from the e.cient market hypothesis in conjunction with the relatively low variation in potentially predictable risk premia over short horizons[ However\ many derivative assets such as equity options have payo} functions that are non!linear in the return on the underlying asset[ For these assets\ tests of the e.cient market hypothesis require knowledge of the full density of the underlying return distribution[ Although return levels are hard to predict\ powers of returns seem to possess stronger pre! dictability and much of the promise of density forecasting stems from this fact[ Often\ the objective function in _nance involves controlling the risk of some portfolio whose return distribution is highly non!Gaussian[ To capture features such as skews and fat tails in return distributions\ a variety of approaches have been considered[ Early papers used fat!tailed Pareto or mixture distributions to unconditional returns[ This unconditional approach was succeeded by the litera! ture on autoregressive conditional heteroscedasticity "ARCH# e}ects which established beyond doubt that the scale of the distribution "as measured by the conditional standard deviation# of Correspondence to]