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Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors

  • Eric Hillebrand

    ()

    (Aarhus University and CREATES)

  • Tae-Hwy Lee

    ()

    (University of California, Riverside)

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.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-18.

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Length: 23
Date of creation: 04 2012
Date of revision:
Handle: RePEc:aah:create:2012-18
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. 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, School of Economics and Management, University of Aarhus.
  2. Todd E. Clark & Michael W. McCracken, 2009. "Combining Forecasts from Nested Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 303-329, 06.
  3. 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.
  4. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
  5. 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.
  6. 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.
  7. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  8. 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.
  9. 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.
  10. 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.
  11. Carter Hill, R. & Judge, George, 1987. "Improved prediction in the presence of multicollinearity," Journal of Econometrics, Elsevier, vol. 35(1), pages 83-100, May.
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