Empirical Bayes Forecasts of One Time Series Using Many Predictors
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.
|Date of creation:||01 Aug 2000|
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- Gary Chamberlain & Guido W. Imbens, 1996.
"Hierarchical Bayes Models with Many Instrumental Variables,"
NBER Technical Working Papers
0204, National Bureau of Economic Research, Inc.
- Chamberlain, Gary & Imbens, Guido, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Scholarly Articles 3221489, Harvard University Department of Economics.
- Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Harvard Institute of Economic Research Working Papers 1781, Harvard - Institute of Economic Research.
- Haerdle,W. & Hart,J.D. & Marron,J.S. & Tsybakov,A.B., 1989.
"Bandwidth choice for average derivative estimation,"
Discussion Paper Serie A
200, University of Bonn, Germany.
- 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).
- James H. Stock & Mark W. Watson, 1999.
NBER Working Papers
7023, National Bureau of Economic Research, Inc.
- Joshua Angrist & Alan Krueger, 1990.
"Does Compulsory School Attendance Affect Schooling and Earnings?,"
653, Princeton University, Department of Economics, Industrial Relations Section..
- 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.
- Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
- Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
- James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
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