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

Author

Listed:
  • Tae-Hwy Lee

    (Department of Economics, University of California Riverside)

  • Yundong Tu

    (Peking University, Beijing, China)

  • Aman Ullah

    (University of California, Riverside)

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.

Suggested Citation

  • Tae-Hwy Lee & Yundong Tu & Aman Ullah, 2014. "Forecasting Equity Premium: Global Historical Average versus Local Historical Average and Constraints," Working Papers 201405, University of California at Riverside, Department of Economics.
  • Handle: RePEc:ucr:wpaper:201405
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    References listed on IDEAS

    as
    1. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    3. John Y. Campbell & Samuel B. Thompson, 2008. "Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1509-1531, July.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, June.
    5. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    6. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
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    Cited by:

    1. Ren, Yu & Tu, Yundong & Yi, Yanping, 2019. "Balanced predictive regressions," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 118-142.
    2. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.
    3. Biqing Cai & Jiti Gao, 2017. "A simple nonlinear predictive model for stock returns," Monash Econometrics and Business Statistics Working Papers 18/17, Monash University, Department of Econometrics and Business Statistics.
    4. Tu, Yundong & Xie, Xinling, 2023. "Penetrating sporadic return predictability," Journal of Econometrics, Elsevier, vol. 237(1).
    5. Guglielmo Maria Caporale & Luis A. Gil-Alana & Miguel Martin-Valmayor, 2021. "Persistence in the market risk premium: evidence across countries," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 45(3), pages 413-427, July.
    6. Lee Tae-Hwy & Wang He & Xi Zhou & Zhang Ru, 2023. "Density Forecast of Financial Returns Using Decomposition and Maximum Entropy," Journal of Econometric Methods, De Gruyter, vol. 12(1), pages 57-83, January.

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    More about this item

    Keywords

    Equity premium; Nonparametric local historical average model; Positivity constraint; Bagging; Model averaging; Semiparametric single index model.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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