Forecasting Using Principal Components From a Large Number of Predictors
James H. StockJames H. Stock is Professor, Kennedy School of Government, Harvard University, Cambridge, MA 02138, and the National Bureau of Economic Research . Mark W. Watson is Professor, Department of Economics and Woodrow Wilson School, Princeton University, Princeton, NJ 08540, and the National Bureau of Economic Research . The results in this article originally appeared in the paper titled “Diffusion Indexes” (NBER Working Paper 6702, August 1998). The authors thank the associate editor and referees, Jushan Bai, Michael Boldin, Frank Diebold, Gregory Chow, Andrew Harvey, Lucrezia Reichlin, Ken Wallis, and Charles Whiteman for helpful discussions and/or comments, and Lewis Chan, Piotr Eliasz, and Alexei Onatski for skilled research assistance. This research was supported in part by National Science Foundation grants SBR-9409629 and SBR-9730489Mark W. WatsonJames H. Stock is Professor, Kennedy School of Government, Harvard University, Cambridge, MA 02138, and the National Bureau of Economic Research . Mark W. Watson is Professor, Department of Economics and Woodrow Wilson School, Princeton University, Princeton, NJ 08540, and the National Bureau of Economic Research . The results in this article originally appeared in the paper titled “Diffusion Indexes” (NBER Working Paper 6702, August 1998). The authors thank the associate editor and referees, Jushan Bai, Michael Boldin, Frank Diebold, Gregory Chow, Andrew Harvey, Lucrezia Reichlin, Ken Wallis, and Charles Whiteman for helpful discussions and/or comments, and Lewis Chan, Piotr Eliasz, and Alexei Onatski for skilled research assistance. This research was supported in part by National Science Foundation grants SBR-9409629 and SBR-9730489
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Аннотация
This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both N and T grow large. The estimated factors are shown to be consistent, even in the presence of time variation in the factor model.
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