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Discriminating between fractional integration and spurious long memory

Author

Listed:
  • Niels Haldrup

    (Aarhus University and CREATES)

  • Robinson Kruse

    (Leibniz University Hannover and CREATES)

Abstract
Fractionally integrated processes have become a standard class of models to describe the long memory features of economic and financial time series data. However, it has been demonstrated in numerous studies that structural break processes and non-linear features can often be confused as being long memory. The question naturally arises whether it is possible empirically to determine the source of long memory as being genuinely long memory in the form of a fractionally integrated process or whether the long range dependence is of a di¤erent nature. In this paper we suggest a testing procedure that helps discriminating between such processes. The idea is based on the feature that nonlinear transformations of stationary fractionally integrated Gaussian processes decrease the order of memory in a speci?c way which is determined by the Hermite rank of the transformation. In principle, a non-linear transformation of the series can make the series short memory I(0). We suggest using the Wald test of Shimotsu (2007) to test the null hypothesis that a vector time series of properly transformed variables is I(0). Our testing procedure is designed such that even non-stationary fractionally integrated processes are permitted under the null hypothesis. The test is shown to have good size and to be robust against certain types of deviations from Gaussianity. The test is also shown to be consistent against a broad class of processes that are non-fractional but still exhibit (spurious) long memory. In particular, the test is shown to have excellent power against a class of stationary and non-stationary random level shift models as well as Markov switching GARCH processes where the break and transition probabilities are allowed to be time varying.

Suggested Citation

  • Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-19
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    File URL: https://repec.econ.au.dk/repec/creates/rp/14/rp14_19.pdf
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    References listed on IDEAS

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    3. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    4. Gil-Alana, Luis A. & Gupta, Rangan, 2014. "Persistence and cycles in historical oil price data," Energy Economics, Elsevier, vol. 45(C), pages 511-516.
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    6. Chevillon, Guillaume & Hecq, Alain & Laurent, Sébastien, 2018. "Generating univariate fractional integration within a large VAR(1)," Journal of Econometrics, Elsevier, vol. 204(1), pages 54-65.
    7. Nima Nonejad, 2019. "Modeling Persistence and Parameter Instability in Historical Crude Oil Price Data Using a Gibbs Sampling Approach," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1687-1710, April.
    8. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    9. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
    10. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2017. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Long memory; fractional integration; non-linear models; structural breaks; random level shifts; Hermite polynomials; realized volatility; in?ation.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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