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Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point

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  • Iacone, Fabrizio
  • Leybourne, Stephen J
  • Taylor, AM Robert

Abstract

We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, and unlike conventional unit root and stationarity tests, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test.

Suggested Citation

  • Iacone, Fabrizio & Leybourne, Stephen J & Taylor, AM Robert, 2017. "Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point," Essex Finance Centre Working Papers 19654, University of Essex, Essex Business School.
    • Handle: RePEc:esy:uefcwp:19654
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    Cited by:

    1. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    2. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    3. Carina Gerstenberger, 2021. "Robust discrimination between long‐range dependence and a change in mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 34-62, January.
    4. Karanasos, Menelaos & Paraskevopoulos, Alexandros & Magdalinos, Anastasios & Canepa, Alessandra, 2024. "A Unified Theory for Arma Models with Varying Coefficients: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202413, University of Turin.

    More about this item

    Keywords

    Fractional integration; trend break; Lagrange multiplier test; asymptotically locally most powerful test;
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