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

Eric Hillebrand () and Tae Hwy Lee
Additional contact information
Eric Hillebrand: Aarhus University and CREATES, Postal: Bartholins Allé 10, 8000 Aarhus C, Denmark

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)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/12/rp12_18.pdf (application/pdf)

Related works:
Chapter: Stein-Rule Estimation and Generalized Shrinkage Methods for Forecasting Using Many Predictors (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2012-18

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by ().