TY  - JOUR
AU  - Knox,Thomas
AU  - Stock,James H.
AU  - Watson,Mark W.
TI  - Empirical Bayes Forecasts of One Time Series Using Many Predictors
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 269
PY  - 2001
Y2  - March 2001
UR  - http://www.nber.org/papers/t0269
L1  - http://www.nber.org/papers/t0269.pdf
N1  - Author contact info:
Thomas Knox
Bracebridge Capital, LLC
One Bow Street
Cambridge, MA 02138
E-Mail: tom@brcap.com

James H. Stock
Department of Economics
Harvard University
Littauer Center M27
Cambridge, MA 02138
Tel: 617/496-0502
Fax: 617/495-7730
E-Mail: James_Stock@harvard.edu

Mark W. Watson
Department of Economics
Princeton University
Princeton, NJ 08544-1013
Tel: 609/258-4811
Fax: 609/258-5533
E-Mail: mwatson@princeton.edu
AB  - 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.
ER  -