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Understanding Spurious Regression in Financial Economics

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  • Ai Deng

Abstract

A new asymptotic framework is used to provide finite sample approximations for various statistics in the spurious return predictive regression analyzed by Ferson, Sarkissian, and Simin (2003a). Our theory explains all the findings of Ferson, Sarkissian, and Simin (2003a) and confirms the theoretical possibility of a spurious regression bias. The theory developed in the article has important implications with respect to existing inferential theories in predictive regressions. We also propose a simple diagnostic test to detect potential spurious regression bias in empirical analysis. The test is applied to four variants of the SP500 monthly stock returns and the six Fama-French benchmark portfolio monthly returns.

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  • Ai Deng, 2014. "Understanding Spurious Regression in Financial Economics," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 122-150.
    • Handle: RePEc:oup:jfinec:v:12:y:2014:i:1:p:122-150.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbs025
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    2. Gerdie Everaert & Hauke Vierke, 2016. "Demographics and Business Cycle Volatility: A Spurious Relationship?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1467-1477, November.
    3. Gourieroux, Christian & Jasiak, Joann, 2010. "Inference for Noisy Long Run Component Process," MPRA Paper 98987, University Library of Munich, Germany.
    4. Lin, Boqiang & Omoju, Oluwasola E., 2017. "Focusing on the right targets: Economic factors driving non-hydro renewable energy transition," Renewable Energy, Elsevier, vol. 113(C), pages 52-63.
    5. Ke-Li Xu & Junjie Guo, 2021. "A New Test for Multiple Predictive Regression," CAEPR Working Papers 2022-001 Classification-C, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    6. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
    7. Docherty, Paul & Hurst, Gareth, 2018. "Return dispersion and conditional momentum returns: International evidence," Pacific-Basin Finance Journal, Elsevier, vol. 50(C), pages 263-278.
    8. Powell, John G. & Shi, Jing & Smith, Tom & Whaley, Robert E., 2009. "Political regimes, business cycles, seasonalities, and returns," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1112-1128, June.
    9. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    10. Shuping Cheng & Lingjie Meng & Weizhong Wang, 2022. "The Impact of Environmental Regulation on Green Energy Technology Innovation—Evidence from China," Sustainability, MDPI, vol. 14(14), pages 1-23, July.
    11. Torben G. Andersen & Rasmus T. Varneskov, 2018. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    12. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.
    13. Ai Deng Author-X-Name-First: Ai, 2006. "Local Power of Andrews and Ploberger Tests Against Nearly Integrated, Nearly White Noise Process," Boston University - Department of Economics - Working Papers Series WP2006-027, Boston University - Department of Economics.
    14. Xu, Bin & Lin, Boqiang, 2016. "Reducing CO2 emissions in China's manufacturing industry: Evidence from nonparametric additive regression models," Energy, Elsevier, vol. 101(C), pages 161-173.
    15. Wang Cindy Shin-Huei & Hafner Christian M., 2018. "A simple solution of the spurious regression problem," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(3), pages 1-14, June.
    16. Hjalmarsson, Erik, 2018. "Maximal predictability under long-term mean reversion," Journal of Empirical Finance, Elsevier, vol. 45(C), pages 269-282.
    17. Deng, Kaihua, 2016. "A refined asymptotic framework for dividend yield in predictive regressions," Economics Letters, Elsevier, vol. 138(C), pages 60-63.
    18. Deng, Ai, 2010. "Local power of consistent tests for serial correlation against the nearly integrated, nearly white noise process," Economics Letters, Elsevier, vol. 107(1), pages 22-25, April.

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    More about this item

    Keywords

    spurious regression; signal-to-noise ratio; fixed-b asymptotics; data mining; stock return predictability;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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