TAILIEUCHUNG - Handbook of Economic Forecasting part 66

Handbook of Economic Forecasting part 66. 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 | 624 . Clements and . Hendry of data to be used for model estimation or lead to the use of rolling windows of observations to allow for gradual change or to the adoption of more flexible models as discussed in Sections 6 and 7. As argued by Chu Stinchcombe and White 1996 the one shot tests discussed so far may not be ideal in a real-time forecasting context as new data accrue. The tests are designed to detect breaks on a given historical sample of a fixed size. Repeated application of the tests as new data becomes available or repeated application retrospectively moving through the historical period will result in the asymptotic size of the sequence of tests approaching one if the null rejection frequency is held constant. Chu Stinchcombe and White 1996 p. 1047 illustrate with reference to the Ploberger Krämer and Kontrus 1989 retrospective fluctuation test. In the simplest case that T is an independent sequence the null of stability in mean is H0 E Tt 0 t 1 2 . versus H1 E Tt 0 for some t. For a given n 1 FLn maxa lyn k n -Y yt k n k t 1 is compared to a critical value c determined from the hitting probability of a Brownian motion. But if FLn is implemented sequentially for n 1 n 2 . then the probability of a type 1 error is one asymptotically. Similarly if a Chow test is repeatedly calculated every time new observations become available. Chu Stinchcombe and White 1996 suggest monitoring procedures for CUSUM and parameter fluctuation tests where the critical values are specified as boundary functions such that they are crossed with the prescribed probability under Hq. The CUSUM implementation is as follows. Define m n 0 m 1 x x _ n . Wi i m where m is the end of the historical period so that monitoring starts at m 1 and n 1. The rni are the recursive residuals rni ei u where ei yi xi ii 1 and - 1 xi I2 xj xj xi j 1 with i -1 i ß i 12 xj xj 72xjyj j 1 j 1 for the model yt x ß Ch. 12 Forecasting with Breaks 625 where xt is k x 1 say and Xj x1. xj etc. a2 is a .

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