Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors
We examine the Stein-rule shrinkage estimator for possible improvements in estimation and forecasting when there are many predictors in a linear time series model. We consider the Stein-rule estimator of Hill and Judge (1987) that shrinks the unrestricted unbiased OLS estimator towards a restricted biased principal component (PC) estimator. Since the Stein-rule estimator combines the OLS and PC estimators, it is a model-averaging estimator and produces a combined forecast. The conditions under which the improvement can be achieved depend on several unknown parameters that determine the degree of the Stein-rule shrinkage. We conduct Monte Carlo simulations to examine these parameter regions. The overall picture that emerges is that the Stein-rule shrinkage estimator can dominate both OLS and principal components estimators within an intermediate range of the signal-to-noise ratio. If the signal-to-noise ratio is low, the PC estimator is superior. If the signal-to-noise ratio is high, the OLS estimator is superior. In out-of-sample forecasting with AR(1) predictors, the Stein-rule shrinkage estimator can dominate both OLS and PC estimators when the predictors exhibit low persistence.
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.:
- Inoue, Atsushi & Kilian, Lutz, 2005. "How Useful is Bagging in Forecasting Economic Time Series? A Case Study of US CPI Inflation," CEPR Discussion Papers 5304, C.E.P.R. Discussion Papers.
- Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
- Hill, R.Carter & Judge, George G, 1990. "Improved estimation under collinearity and squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 296-312, February.
- Eric Hillebrand & Huiyu Huang & Tae-Hwy Lee & Canlin Li, 2011. "Using the Yield Curve in Forecasting Output Growth and In?flation," CREATES Research Papers 2012-17, Department of Economics and Business Economics, Aarhus University.
- Bair, Eric & Hastie, Trevor & Paul, Debashis & Tibshirani, Robert, 2006. "Prediction by Supervised Principal Components," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 119-137, March.
- Todd E. Clark & Michael W. McCracken, 2007.
"Combining forecasts from nested models,"
Finance and Economics Discussion Series
2007-43, Board of Governors of the Federal Reserve System (U.S.).
- Todd E. Clark & Michael W. McCracken, 2008. "Combining forecasts from nested models," Working Papers 2008-037, Federal Reserve Bank of St. Louis.
- Todd E. Clark & Michael W. McCracken, 2006. "Combining forecasts from nested models," Research Working Paper RWP 06-02, Federal Reserve Bank of Kansas City.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- Mittelhammer, Ron C., 1985. "Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints," Journal of Econometrics, Elsevier, vol. 29(3), pages 289-303, September.
- Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
- Carter Hill, R. & Judge, George, 1987. "Improved prediction in the presence of multicollinearity," Journal of Econometrics, Elsevier, vol. 35(1), pages 83-100, May.
- Fomby, Thomas B & Samanta, Subarna K, 1991. "Application of Stein Rules to Combination Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 391-407, October.
When requesting a correction, please mention this item's handle: RePEc:aah:create:2012-18. 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: ()
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.