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Long‐Run and Cyclical Dynamics in the US Stock Market

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  • Guglielmo Maria Caporale
  • Luis Gil‐Alana

Abstract

ABSTRACT This paper uses fractional integration to examine the long‐run dynamics and cyclical structure of US inflation, real risk‐free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 2000. It implements a procedure which allows consideration of unit roots with possibly fractional orders of integration both at zero (long‐run) and cyclical frequencies. When focusing exclusively on the former, the estimated order of integration varies considerably, and non‐stationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long‐run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, six different criteria are applied to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results, based on a 15‐year horizon, show that the former outperforms the others in a number of cases. Copyright © 2013 John Wiley & Sons, Ltd.

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  • Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    • Handle: RePEc:wly:jforec:v:33:y:2014:i:2:p:147-161
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    Cited by:

    1. Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, May.
    2. Guglielmo Maria Caporale & Luis Gil-Alana, 2010. "Multiple cyclical fractional structures in financial time series," Applied Economics Letters, Taylor & Francis Journals, vol. 17(11), pages 1079-1081.
    3. Rania Jammazi & Chaker Aloui, 2014. "Cyclical components and dual long memory in the foreign exchange rate dynamics: the Tunisian case," Working Papers 2014-198, Department of Research, Ipag Business School.
    4. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2010. "The Weekly Structure of US Stock Prices," CESifo Working Paper Series 3245, CESifo.
    5. Caporale, Guglielmo Maria & Gil-Alana, Luis A. & Poza, Carlos, 2020. "Persistence, non-linearities and structural breaks in European stock market indices," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 50-61.
    6. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2020. "Modeling US historical time-series prices and inflation using alternative long-memory approaches," Empirical Economics, Springer, vol. 58(4), pages 1491-1511, April.
    7. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2011. "Long Memory and Fractional Integration in High-Frequency British Pound / Dollar Spot Exchange Rates," Faculty Working Papers 02/11, School of Economics and Business Administration, University of Navarra.
    8. Giorgio Canarella & Luis Gil-Alana & Rangan Gupta & Stephen M Miller, 2021. "Persistence and cyclical dynamics of US and UK house prices: Evidence from over 150 years of data," Urban Studies, Urban Studies Journal Limited, vol. 58(1), pages 53-72, January.
    9. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2013. "Long memory and fractional integration in high frequency data on the US dollar/British pound spot exchange rate," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 1-9.
    10. Guglielmo Maria Caporale & Luis A. Gil-Alana & Carlos Poza, 2021. "Cycles and Long-Range Behaviour in the European Stock Markets," Dynamic Modeling and Econometrics in Economics and Finance, in: Gilles Dufrénot & Takashi Matsuki (ed.), Recent Econometric Techniques for Macroeconomic and Financial Data, pages 293-302, Springer.
    11. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.
    12. Harvey, David I. & Leybourne, Stephen J. & Whitehouse, Emily J., 2017. "Forecast evaluation tests and negative long-run variance estimates in small samples," International Journal of Forecasting, Elsevier, vol. 33(4), pages 833-847.
    13. Luis A. Gil-Alana & Yun Cao, 2011. "Stock market prices in China. Efficiency, mean reversion, long memory volatility and other implicit dynamics," Faculty Working Papers 12/11, School of Economics and Business Administration, University of Navarra.
    14. Boubaker, Heni & Sghaier, Nadia, 2015. "Semiparametric generalized long-memory modeling of some mena stock market returns: A wavelet approach," Economic Modelling, Elsevier, vol. 50(C), pages 254-265.
    15. Souhir Ben Amor & Heni Boubaker & Lotfi Belkacem, 2022. "Predictive Accuracy of a Hybrid Generalized Long Memory Model for Short Term Electricity Price Forecasting," Papers 2204.09568, arXiv.org.
    16. repec:dau:papers:123456789/6913 is not listed on IDEAS
    17. Beaumont, Paul & Smallwood, Aaron, 2019. "Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models," MPRA Paper 96314, University Library of Munich, Germany.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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