Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors
AbstractWe 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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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-18.
Date of creation: 04 2012
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Web page: http://www.econ.au.dk/afn/
Stein-rule; shrinkage; risk; variance-bias tradeo; OLS; principal components.;
Find related papers by JEL classification:
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
- NEP-ECM-2012-05-15 (Econometrics)
- NEP-ETS-2012-05-15 (Econometric Time Series)
- NEP-FOR-2012-05-15 (Forecasting)
- NEP-ORE-2012-05-15 (Operations Research)
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