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Boundaries of Predictability: Noisy Predictive Regressions

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  • Torous, Walter
  • Valkanov, Rossen

Abstract

Even if returns are truly forecasted by variables such as the dividend yield, the noise in such a predictive regression may overwhelm the signal of the conditioning variable and render estimation, inference and forecasting unreliable. Unfortunately, traditional asymptotic approximations are not suitable to investigate the small sample properties of forecasting regressions with excessive noise. To systematically analyze predictive regressions, it is useful to quantify a forecasting variable’s signal relative to the noisiness of returns in a given sample. We define an index of signal strength, or information accumulation, by renormalizing the signal-noise ratio. The novelty of our parameterization is that this index explicitly influences rates of convergence and can lead to inconsistent estimation and testing, unreliable R2s, and no out-of-sample forecasting power. Indeed, we prove that if the signal-noise ratio is close to zero, as is the case for many of the explanatory variables previously suggested in the finance literature, model based forecasts will do no better than the corresponding simple unconditional mean return. Our analytic framework is general enough to capture most of the previous findings surrounding predictive regressions using dividend yields and other persistent forecasting variables.

Suggested Citation

  • Torous, Walter & Valkanov, Rossen, 2000. "Boundaries of Predictability: Noisy Predictive Regressions," University of California at Los Angeles, Anderson Graduate School of Management qt33p7672z, Anderson Graduate School of Management, UCLA.
  • Handle: RePEc:cdl:anderf:qt33p7672z
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    References listed on IDEAS

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    1. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-679, June.
    2. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-179, March.
    3. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    4. Bossaerts, Peter & Hillion, Pierre, 1999. "Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn?," Review of Financial Studies, Society for Financial Studies, vol. 12(2), pages 405-428.
    5. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
    6. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
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    Cited by:

    1. Kim, Chang Sik & Lee, Sungro, 2011. "Spurious regressions driven by excessive volatility," Economics Letters, Elsevier, vol. 113(3), pages 292-297.
    2. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    3. Shang, Hua, 2013. "Inference in asset pricing models with a low-variance factor," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 1046-1060.
    4. Clark, Todd E. & McCracken, Michael W., 2012. "In-sample tests of predictive ability: A new approach," Journal of Econometrics, Elsevier, vol. 170(1), pages 1-14.
    5. Bansal, Ravi & Khatchatrian, Varoujan & Yaron, Amir, 2005. "Interpretable asset markets?," European Economic Review, Elsevier, vol. 49(3), pages 531-560, April.
    6. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    7. Deng, Kaihua, 2016. "A refined asymptotic framework for dividend yield in predictive regressions," Economics Letters, Elsevier, vol. 138(C), pages 60-63.
    8. Peter C. B. Phillips, 2015. "Halbert White Jr. Memorial JFEC Lecture: Pitfalls and Possibilities in Predictive Regression†," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(3), pages 521-555.

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