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Boundaries of Predictability: Noisy Predictive Regressions

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Author Info
Walter Torous (Anderson School of Management)
Rossen Valkanov (Anderson School of Management)
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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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 1081.

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Date of creation: 01 Dec 2000
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Handle: RePEc:cdl:anderf:1081

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Christopher L. Cavanagh & Graham Elliott & James Stock, 1995. "Inference in Models with Nearly Integrated Regressors," University of California at San Diego, Economics Working Paper Series 95-29, Department of Economics, UC San Diego.
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  3. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July. [Downloadable!] (restricted)
  4. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December. [Downloadable!] (restricted)
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  6. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  7. 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. [Downloadable!] (restricted)
  8. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(3), pages 195-228. [Downloadable!] (restricted)
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  9. Pierre Perron & Robert J. Shiller, 1984. "Testing the Random Walk Hypothesis: Power Versus Frequency of Observation," Cowles Foundation Discussion Papers 732, Cowles Foundation, Yale University. [Downloadable!]
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  10. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March. [Downloadable!] (restricted)
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  11. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July. [Downloadable!] (restricted)
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  12. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. Bossaerts, Peter & Hillion, Pierre, 1999. "Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn?," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(2), pages 405-28.
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  16. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
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  17. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  18. Perron,P., 1988. "Testing For A Random Walk: A Simulation Experiment Of Power When The Simpling Interval Is Varied," Papers 336, Princeton, Department of Economics - Econometric Research Program.
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  20. Wayne E. Ferson & Sergei Sarkissian & Timothy Simin, 2002. "Spurious Regressions in Financial Economics?," NBER Working Papers 9143, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ai Deng, 2005. "Understanding Spurious Regression in Financial Economics," Boston University - Department of Economics - Working Papers Series WP2005-048, Boston University - Department of Economics. [Downloadable!]
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