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Boundaries of Predictability: Noisy Predictive Regressions

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  • Torous, Walter
  • Valkanov, Rossen
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    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.

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    File URL: http://www.escholarship.org/uc/item/33p7672z.pdf;origin=repeccitec
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    Bibliographic Info

    Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number qt33p7672z.

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    Date of creation: 01 Dec 2000
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    Handle: RePEc:cdl:anderf:qt33p7672z

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    1. Campbell, John, 1991. "A Variance Decomposition for Stock Returns," Scholarly Articles 3207695, Harvard University Department of Economics.
    2. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-79, June.
    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. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
    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. 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 405-28.
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    Cited by:
    1. Todd E. Clark & Michael W. McCracken, 2009. "In-sample tests of predictive ability: a new approach," Research Working Paper RWP 09-10, Federal Reserve Bank of Kansas City.
    2. Bansal, Ravi & Khatchatrian, Varoujan & Yaron, Amir, 2005. "Interpretable asset markets?," European Economic Review, Elsevier, vol. 49(3), pages 531-560, April.
    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. Amit Goval & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," NBER Working Papers 10483, National Bureau of Economic Research, Inc.
    5. 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.

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