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Forecasting Equity Premium: Global Historical Average versus Local Historical Average and Constraints

Tae Hwy Lee, Yundong Tu and Aman Ullah

No 201405, Working Papers from University of California at Riverside, Department of Economics

Abstract: The equity premium, return on equity minus return on risk-free asset, is expected to be positive. We consider imposing such positivity constraint in local historical average (LHA) in nonparametric kernel regression framework. It is also extended to the semiparametric single index model when multiple predictors are used. We construct the constrained LHA estimator via an indicator function which operates as `model-selection' between the unconstrained LHA and the bound of the constraint (zero for the positivity constraint). We smooth the indicator function by bagging (Breiman 1996a), which operates as `model-averaging' and yields a combined forecast of unconstrained LHA forecasts and the bound of the constraint. The local combining weights are determined by the probability that the constraint is binding. Asymptotic properties of the constrained LHA estimators without and with bagging are established, which show how the positive constraint and bagging can help reduce the asymptotic variance and mean squared errors. Monte Carlo simulations are conducted to show the finite sample behavior of the asymptotic properties. In predicting U.S. equity premium, we show that substantial nonlinearity can be captured by LHA and that the local positivity constraint can improve out-of-sample prediction of the equity premium.

Keywords: Equity premium; Nonparametric local historical average model; Positivity constraint; Bagging; Model averaging; Semiparametric single index model. (search for similar items in EconPapers)
JEL-codes: C14 C50 C53 G17 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-for and nep-ger
Date: 2014-09
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Forthcoming, Journal of Business and Economic Statistics.

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http://economics.ucr.edu/repec/ucr/wpaper/201405.pdf First version, 2014 (application/pdf)

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Journal Article: Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints (2015) Downloads
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