IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Empirical Bayes Forecasts of One Time Series Using Many Predictors

Listed author(s):
  • Thomas Knox

    (Harvard University)

  • James H. Stock

    (Harvard University)

  • Mark W. Watson

    (Princeton University and NBER)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: main text
Download Restriction: no

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

in new window

Date of creation: 01 Aug 2000
Handle: RePEc:ecm:wc2000:1421
Contact details of provider: Phone: 1 212 998 3820
Fax: 1 212 995 4487
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
  2. HÄRDLE, Wolfgang & HART, Jeffrey & MARRON, Steve & TSYBAKOV, Alexander, "undated". "Bandwith choice for average derivative estimation," CORE Discussion Papers RP 977, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Chamberlain, Gary & Imbens, Guido, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Scholarly Articles 3221489, Harvard University Department of Economics.
  4. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
  5. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
  6. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ecm:wc2000:1421. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.