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

Eric Hillebrand and Tae Hwy Lee

A chapter in 30th Anniversary Edition, 2012, pp 171-196 from Emerald Group Publishing Limited

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 ordinary least squares (OLS) estimator toward 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 tradeoff; OLS; principal components (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-9053(2012)0000030011

DOI: 10.1108/S0731-9053(2012)0000030011

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