TAILIEUCHUNG - Handbook of Economic Forecasting part 76

Handbook of Economic Forecasting part 76. 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 | 724 . Pesaran and M. Weale where T denotes convergence in quadratic means. Therefore average consensus or market rationality can hold even if the underlying individual expectations are nonrational in the sense of The above conditions allow for a high degree of heterogeneity of expectations and are compatible with individual expectations errors being biased and serially correlated As we shall see this result is particularly relevant to tests of the REH that are based on survey responses. . Extrapolative models of expectations formation In addition to the REH a wide variety of expectations formation models has been advanced in the literature with differing degrees of informational requirements. Most of these models fall under the extrapolative category where point expectations are determined by weighted averages of past realizations. A general extrapolative formula is given by Ei xt i Qit isxt-s 9 where the coefficient matrices is are assumed to be absolute summable subject to the adding up condition œ E is i - 1 s 0 This condition ensures that unconditionally expectations and observations have the same means. For example suppose that xt follows the first-order stationary autoregressive process unknown to the individuals Xt fl Xt-1 St where all eigenvalues of lie inside the unit circle. It is then easily seen that 00 J2 ij i - -1 s 0 and under the adding up condition 10 yields E Ei xt 1 Q E xt I - -1g. Under 10 time averages of extrapolative expectations will be the same as the sample mean of the underlying processes an implication that can be tested using quantitative survey expectations if available. 7 The term consensus forecasts or expectations was popularized by Joseph Livingston the founder of the Livingston Survey in the . See Section 3 for further details and references. Ch. 14 Survey Expectations 725 The average or consensus version of the extrapolative hypothesis derived using the weights wit defined by 6 has also the extrapolative form E xt

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