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The scale of predictability

Author

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  • Federico M. Bandi
  • Bernard Perron
  • Andrea Tamoni
  • Claudio Tebaldi

Abstract

We view economic time series as the result of a cascade of shocks occurring at different times and different frequencies (scales). We suggest that economic relations that are found to be elusive when using raw data may hold true for different layers (details) in the cascade of economic shocks. This observation leads to a notion of a scale-specific predictability. Using direct extraction of the details and two-way aggregation, we provide strong evidence of risk compensations in market returns, as well as of an unusually clear link between macroeconomic uncertainty and uncertainty in financial markets, at frequencies lower than the business cycle. JEL classification: C22, E32, E44, G12, G17 Keywords: long run, predictability, aggregation, risk-return trade-off, Fisher hypothesis.

Suggested Citation

  • Federico M. Bandi & Bernard Perron & Andrea Tamoni & Claudio Tebaldi, 2014. "The scale of predictability," Working Papers 509, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  • Handle: RePEc:igi:igierp:509
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    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. Calvet, Laurent E. & Fisher, Adlai J., 2007. "Multifrequency news and stock returns," Journal of Financial Economics, Elsevier, vol. 86(1), pages 178-212, October.
    3. Owen Lamont, 1998. "Earnings and Expected Returns," Journal of Finance, American Finance Association, vol. 53(5), pages 1563-1587, October.
    4. Nelson, Charles R, 1976. "Inflation and Rates of Return on Common Stocks," Journal of Finance, American Finance Association, vol. 31(2), pages 471-483, May.
    5. Cai, Zongwu & Wang, Yunfei, 2014. "Testing predictive regression models with nonstationary regressors," Journal of Econometrics, Elsevier, vol. 178(P1), pages 4-14.
    6. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    7. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    8. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    9. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    10. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    11. Simone Cerreia-Vioglio & Fulvio Ortu & Federico Severino & Claudio Tebaldi, 2017. "Multivariate Wold Decompositions," Working Papers 606, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    13. Andrew B. Abel, 2003. "The Effects of a Baby Boom on Stock Prices and Capital Accumulation in the Presence of Social Security," Econometrica, Econometric Society, vol. 71(2), pages 551-578, March.
    14. Bansal, Ravi & Khatchatrian, Varoujan & Yaron, Amir, 2005. "Interpretable asset markets?," European Economic Review, Elsevier, vol. 49(3), pages 531-560, April.
    15. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    16. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Inflation Illusion and Stock Prices," American Economic Review, American Economic Association, vol. 94(2), pages 19-23, May.
    17. Natalia Sizova, 2013. "Long-Horizon Return Regressions With Historical Volatility and Other Long-Memory Variables," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 546-559, October.
    18. John T. Scruggs, 1998. "Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach," Journal of Finance, American Finance Association, vol. 53(2), pages 575-603, April.
    19. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    20. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
    21. Diego Comin & Mark Gertler, 2006. "Medium-Term Business Cycles," American Economic Review, American Economic Association, vol. 96(3), pages 523-551, June.
    22. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    23. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    24. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    25. Francis X. Diebold & Kamil Yılmaz, 2007. "Macroeconomic Volatility and Stock Market Volatility,World-Wide," Koç University-TUSIAD Economic Research Forum Working Papers 0711, Koc University-TUSIAD Economic Research Forum.
    26. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    27. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    28. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    29. Martin Lettau & Sydney Ludvigson, 2001. "Consumption, Aggregate Wealth, and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 815-849, June.
    30. Andreas Fuster & David Laibson & Brock Mendel, 2010. "Natural Expectations and Macroeconomic Fluctuations," Journal of Economic Perspectives, American Economic Association, vol. 24(4), pages 67-84, Fall.
    31. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    32. Ľuboš Pástor & Robert F. Stambaugh, 2009. "Predictive Systems: Living with Imperfect Predictors," Journal of Finance, American Finance Association, vol. 64(4), pages 1583-1628, August.
    33. Scott R. Baker & Nicholas Bloom & Steven J. Davis, 2016. "Measuring Economic Policy Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1593-1636.
    34. Author-Name: John Geanakoplos & Michael Magill & Martine Quinzii, 2004. "Demography and the Long-Run Predictability of the Stock Market," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(1), pages 241-326.
    35. Mishkin, Frederic S., 1992. "Is the Fisher effect for real? : A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 195-215, November.
    36. Pedro Santa‐Clara & Rossen Valkanov, 2003. "The Presidential Puzzle: Political Cycles and the Stock Market," Journal of Finance, American Finance Association, vol. 58(5), pages 1841-1872, October.
    37. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    38. Michael Magill, 2004. "Demography and the Stock Market," Theory workshop papers 658612000000000080, UCLA Department of Economics.
    39. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    40. Fulvio Ortu & Andrea Tamoni & Claudio Tebaldi, 2013. "Long-Run Risk and the Persistence of Consumption Shocks," The Review of Financial Studies, Society for Financial Studies, vol. 26(11), pages 2876-2915.
    41. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2003. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," American Economic Review, American Economic Association, vol. 93(1), pages 38-62, March.
    42. John H. Cochrane, 2008. "The Dog That Did Not Bark: A Defense of Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1533-1575, July.
    43. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    44. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    45. Bonomo, Marco & Garcia, René & Meddahi, Nour & Tédongap, Roméo, 2015. "The long and the short of the risk-return trade-off," Journal of Econometrics, Elsevier, vol. 187(2), pages 580-592.
    46. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    47. Gençay, Ramazan & Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon J., 2001. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics," Elsevier Monographs, Elsevier, edition 1, number 9780122796708.
    48. Bandi, Federico M. & Perron, Benoît, 2008. "Long-run risk-return trade-offs," Journal of Econometrics, Elsevier, vol. 143(2), pages 349-374, April.
    49. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    50. Luboš Pástor & Pietro Veronesi, 2009. "Technological Revolutions and Stock Prices," American Economic Review, American Economic Association, vol. 99(4), pages 1451-1483, September.
    51. Bryan Kelly & Seth Pruitt, 2013. "Market Expectations in the Cross-Section of Present Values," Journal of Finance, American Finance Association, vol. 68(5), pages 1721-1756, October.
    52. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
    53. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    54. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    55. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
    56. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.
    57. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    58. Fisher, Mark E & Seater, John J, 1993. "Long-Run Neutrality and Superneutrality in an ARIMA Framework," American Economic Review, American Economic Association, vol. 83(3), pages 402-415, June.
    59. Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 2008. "The Myth of Long-Horizon Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1577-1605, July.
    60. Bart Hobijn & Boyan Jovanovic, 2001. "The Information-Technology Revolution and the Stock Market: Evidence," American Economic Review, American Economic Association, vol. 91(5), pages 1203-1220, December.
    61. Boudoukh, Jacob & Richardson, Matthew, 1993. "Stock Returns and Inflation: A Long-Horizon Perspective," American Economic Review, American Economic Association, vol. 83(5), pages 1346-1355, December.
    62. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    63. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
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    More about this item

    Keywords

    long run; predictability; aggregation; risk-return trade-off; fisher hypothesis.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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