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A Long-Memory Model for Multiple Cycles with an Application to the S&P500

Author

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  • Guglielmo Maria Caporale
  • Luis Alberiko Gil-Alana

Abstract

This paper proposes a long-memory model including multiple cycles in addition to the long-run component. Specifically, instead of a single pole or singularity in the spectrum, it allows for multiple poles and thus different cycles with different degrees of persistence. It also incorporates non-linear deterministic structures in the form of Chebyshev polynomials in time. Simulations are carried out to analyse the finite sample properties of the proposed test, which is shown to perform well in the case of a relatively large sample with at least 1000 observations. The model is then applied to weekly data on the S&P500 from 1 January 1970 to 26 October 2023 as an illustration. The estimation results based on the first differenced logged values (i.e., the returns) point to the existence of three cyclical structures in the series with a length of approximately one month, one year and four years respectively, and to orders of integration in the range (0, 0.20), which implies stationary long memory in all cases.

Suggested Citation

  • Guglielmo Maria Caporale & Luis Alberiko Gil-Alana, 2024. "A Long-Memory Model for Multiple Cycles with an Application to the S&P500," CESifo Working Paper Series 10947, CESifo.
    • Handle: RePEc:ces:ceswps:_10947
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    References listed on IDEAS

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    4. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    5. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    fractional integration; multiple cycles; stock market indices; S&P500;
    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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