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Time series forecasting by principal covariate regression

  • Heij, C.
  • Groenen, P.J.F.
  • van Dijk, D.J.C.

This paper is concerned with time series forecasting in the presence of a large number of predictors. The results are of interest, for instance, in macroeconomic and financial forecasting where often many potential predictor variables are available. Most of the current forecast methods with many predictors consist of two steps, where the large set of predictors is first summarized by means of a limited number of factors -for instance, principal components- and, in a second step, these factors and their lags are used for forecasting. A possible disadvantage of these methods is that the construction of the components in the first step is not directly related to their use in forecasting in the second step. This motivates an alternative method, principal covariate regression (PCovR), where the two steps are combined in a single criterion. This method has been analyzed before within the framework of multivariate regression models. Moti- vated by the needs of macroeconomic time series forecasting, this paper discusses two adjustments of standard PCovR that are necessary to allow for lagged factors and for preferential predictors. The resulting nonlinear estimation problem is solved by means of a method based on iterative majorization. The paper discusses some numerical aspects and analyzes the method by means of simulations. Further, the empirical per- formance of PCovR is compared with that of the two-step principal component method by applying both methods to forecast four US macroeconomic time series from a set of 132 predictors, using the data set of Stock and Watson (2005).

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File URL: http://repub.eur.nl/pub/8003/ei2006-37.pdf
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Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2006-37.

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Date of creation: 31 Aug 2006
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Handle: RePEc:ems:eureir:8003
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Web page: http://www.eur.nl/ese

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  1. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  2. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(01), pages 3-20, February.
  3. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
  4. Henk Kiers, 1990. "Majorization as a tool for optimizing a class of matrix functions," Psychometrika, Springer, vol. 55(3), pages 417-428, September.
  5. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  6. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  7. Marc Hallin & Mario Forni & Marco Lippi & Lucrezia Reichlin, 2003. "Do financial variables help forecasting inflation and real activity in the Euro area ?," ULB Institutional Repository 2013/2123, ULB -- Universite Libre de Bruxelles.
  8. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(01), pages 60-68, February.
  9. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
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