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Empirical Bayes Forecasts of One Time Series Using Many Predictors

  • Thomas Knox
  • James H. Stock
  • Mark W. Watson

We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their prior. Asymptotically, when K is proportional to T the empirical Bayes estimator is shown to be: (i) optimal in Robbins' (1955, 1964) sense; (ii) the minimum risk equivariant estimator; and (iii) minimax in both the frequentist and Bayesian problems over a class of nonGaussian error distributions. Also, the asymptotic frequentist risk of the minimum risk equivariant estimator is shown to equal the Bayes risk of the (infeasible subjectivist) Bayes estimator in the Gaussian case, where the 'prior' is the weak limit of the empirical cdf of the true parameter values. Monte Carlo results are encouraging. The new estimators are used to forecast monthly postwar U.S. macroeconomic time series using the first 151 principal components from a large panel of predictors.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0269.

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Date of creation: Mar 2001
Date of revision:
Handle: RePEc:nbr:nberte:0269
Note: TWP
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  1. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
  2. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
  3. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  4. Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," NBER Technical Working Papers 0204, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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).
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