This Chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed. And a variety of different specifications and model evaluation tests due to various authors including Christoffersen and...

This paper addresses the notion that many fractional I(d) processes may fall into the empty boxʺ category, as discussed in Granger (1999). We present ex ante forecasting evidence based on an updated version of the absolute returns series examined by Ding, Granger and Engle (1993) that suggests...

This paper outlines testing procedures for assessing the relative out-of-sample predictive accuracy of multiple conditional distribution models. The tests that are discussed are based on either the comparison of entire conditional distributions or the comparison of predictive confidence...

In this paper, we provide new evidence on the empirical usefulness of various simple seasonal models, and underscore the importance of carefully designing criteria by which one judges alternative models. In particular, we underscore the importance of both choice of forecast or simulation horizon...

In this paper, we propose and evaluate a shrinkage based methodology that is designed to improve the accuracy of forecasts of daily integrated volatility. Our approach is based on a two-step shrinkage procedure designed to extract latent common volatility factors from a large dimensional and...

The development of new tests and methods used in the evaluation of time series forecasts and forecasting models remains as important today as it has for the last 50 years. Paraphrasing what Sir Clive W.J. Granger (arguably the father of modern day time series forecasting) said in the 1990s at a...