Empirical Bayes Forecasts of One Time Series Using Many Predictors
AbstractWe 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 InfoPaper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1421.
Date of creation: 01 Aug 2000
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Other versions of this item:
- Thomas Knox & James H. Stock & Mark W. Watson, 2001. "Empirical Bayes Forecasts of One Time Series Using Many Predictors," NBER Technical Working Papers 0269, National Bureau of Economic Research, Inc.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
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- 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 Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
- 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.
- Stock, James H. & Watson, Mark W., 1999.
Journal of Monetary Economics,
Elsevier, vol. 44(2), pages 293-335, October.
- James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
- Chamberlain, Gary & Imbens, Guido, 1996.
"Hierarchical Bayes Models with Many Instrumental Variables,"
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.
- Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," NBER Technical Working Papers 0204, 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.
- Ben S. Bernanke & Jean Boivin, 2001.
"Monetary Policy in a Data-Rich Environment,"
NBER Working Papers
8379, National Bureau of Economic Research, Inc.
- Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society.
- Todd E. Clark, 2000.
"Can out-of-sample forecast comparisons help prevent overfitting?,"
Research Working Paper
RWP 00-05, Federal Reserve Bank of Kansas City.
- 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.
- Gary Koop & Simon Potter, 2003.
"Forecasting in Large Macroeconomic Panels using Bayesian Model Averaging,"
Discussion Papers in Economics
04/16, Department of Economics, University of Leicester.
- 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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