TAILIEUCHUNG - Handbook of Economic Forecasting part 73

Handbook of Economic Forecasting part 73. 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 | 694 E. Ghysels et al. way such that for iSn s e 0 1 6 0 1 0 q v 1 - q v 64 1 1 - p v p v where the transition probabilities q - and p - are allowed to change with the season. When p - p and q - q we obtain the standard homogeneous Markov chain model considered by Hamilton. However if for at least one season the transition probability matrix differs we have a situation where a regime shift will be more or less likely depending on the time of the year. Since iSn s t 0 1 consider the mean shift function p it v ao aiisn s 1 0. 65 Hence the process ySn s has a mean shift a0 in state 1 iSn s 0 and a0 a1 in state 2. These above equations are a version of Hamilton s model with a periodic stochastic switching process. If state 1 with low mean drift is called a recession and state 2 an expansion then we stay in a recession or move to an expansion with a probability scheme that depends on the season. The structure presented so far is relatively simple yet as we shall see some interesting dynamics and subtle interdependencies emerge. It is worth comparing the AR 1 model with a periodic Markovian stochastic switching regime structure and the more conventional linear ARMA processes as well as periodic ARMA models. Let us perhaps start by briefly explaining intuitively what drives the connections between the different models. The model with ySn s typically representing a growth series is covariance stationary under suitable regularity conditions discussed in Ghysels 2000 . Consequently the process has a linear Wold MA representation. Yet the time series model provides a relatively parsimonious structure which determines nonlinearly predictable MA innovations. In fact there are two layers beneath the Wold MA representation. One layer relates to hidden periodicities as described in Tiao and Grupe 1980 or Hansen and Sargent 1993 for instance. Typically such hidden periodicities can be uncovered via augmentation of the state space with the augmented system having a linear .

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