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

Eric Hillebrand () and Tae Hwy Lee

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: 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.

Keywords: Stein-rule; shrinkage; risk; variance-bias tradeo; OLS; principal components. (search for similar items in EconPapers)
JEL-codes: C1 C2 C5 (search for similar items in EconPapers)
Pages: 23
Date: 2012
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Chapter: Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2012-18

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