Handbook of Economic Forecasting part 24. Research on forecasting methods has made important progress over recent years and these developments are brought together in the Handbook of Economic Forecasting. The handbook covers developments in how forecasts are constructed based on multivariate time-series models, dynamic factor models, nonlinear models and combination methods. The handbook also includes chapters on forecast evaluation, including evaluation of point forecasts and probability forecasts and contains chapters on survey forecasts and volatility forecasts. Areas of applications of forecasts covered in the handbook include economics, finance and marketing | 204 V Corradi and . Swanson problem Bai 2003 uses a novel approach based on a martingalization argument to construct a modified Kolmogorov test which has a nuisance parameter free limiting distribution. This test has power against violations of uniformity but not against violations of independence see below for further discussion . Hong 2001 proposes another related interesting test based on the generalized spectrum which has power against both uniformity and independence violations for the case in which the contribution of parameter estimation error vanishes asymptotically. If the null is rejected Hong 2001 also proposes a test for uniformity robust to non independence which is based on the comparison between a kernel density estimator and the uniform density. All of these tests are discussed in detail below. In summary two features differentiate the tests of Corradi and Swanson 2006a CS from the tests outlined in the other papers mentioned above. First CS assume strict stationarity. Second CS allow for dynamic misspecification under the null hypothesis. The second feature allows CS to obtain asymptotically valid critical values even when the conditioning information set does not contain all of the relevant past history. More precisely assume that we are interested in testing for correct specification given a particular information set which may or may not contain all of the relevant past information. This is important when a Kolmogorov test is constructed as one is generally faced with the problem of defining 3t _1. If enough history is not included then there may be dynamic misspecification. Additionally finding out how much information . how many lags to include may involve pre-testing hence leading to a form of sequential test bias. By allowing for dynamic misspecification such pre-testing is not required. To be more precise critical values derived under correct specification given 3t _1 are not in general valid in the case of correct specification given
