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Empirical Bayes Forecasts of One Time Series Using Many Predictors

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  • Thomas Knox

    (Harvard University)

  • James H. Stock

    (Harvard University)

  • Mark W. Watson

    (Princeton University and NBER)

Abstract

We consider the problem of forecasting a single time series, y(t+1), using a linear regression model with k predictor variables, X(t), when each predictor makes a small but nonzero marginal contribution to the forecast. It is well known that OLS is inadmissable when k is at least 3. Although Bayes estimators are admissable, the associated forecasts are unappealing because they can have large (frequentist) risk for some parameter values. We therefore consider Empirical Bayes estimators of the regression coefficients and their associated forecasts, when both the prior and regression error distributions are unknown. To focus attention on large k, we adopt a nesting where k is proportional to the sample size (T), and focus on the asymptotic properties of the true Bayes, Empirical Bayes, and OLS forecasts. We consider Bayes estimators that are functions of the OLS estimates, and propose a nonparametric Empirical Bayes estimator that is asymptotically optimal, in the sense that it achieves the Bayes risk of the best infeasible Bayes estimator when the true error distribution is normal. This result suggests that the Empirical Bayes estimator will have desirable frequentist risk as well. Both nonparametric and parametric Empirical Bayes estimators are examined in a Monte Carlo experiment, with results that are encouraging from both a Bayes and frequentist risk perspective. The new estimators are then applied to the problem of forecasting a few monthly postwar aggregate U.S. economic time series using the first 146 principal components from a large panel of predictor variables.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1421.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1421

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  1. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  2. Hardle, W. & Hart, J. & Marron, J. & Tsybakov, A., 1991. "Bandwidth choice for average derivative estimation," CORE Discussion Papers 1991049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," NBER Technical Working Papers 0204, National Bureau of Economic Research, Inc.
  4. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November.
  5. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  6. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
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Cited by:
  1. Bernanke, Ben S. & Boivin, Jean, 2003. "Monetary policy in a data-rich environment," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 525-546, April.
  2. Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society.
  3. Todd E. Clark, 2004. "Can out-of-sample forecast comparisons help prevent overfitting?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 115-139.
  4. Gary Koop & Simon Potter, 2003. "Forecasting in large macroeconomic panels using Bayesian Model Averaging," Staff Reports 163, Federal Reserve Bank of New York.

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