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Testing the order of fractional integration when smooth deterministic trends are possibly present

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  • Mustafa R. K{i}l{i}nc{c}
  • Michael Massmann

Abstract

This paper introduces a test for fractional integration in a model that possibly contains smooth deterministic trends. We model the trend component using a Chebyshev polynomial and specify the short-run dynamics semi-parametrically, accommodating a broad class of possibly nonlinear processes, including those with conditional heteroskedasticity. We use a local Whittle approach for constructing a Lagrange multiplier test statistic and for constructing a frequency-domain information criterion for the selection of the order of the Chebyshev polynomial. We show that widely used time-domain information criteria are generally inconsistent for the true order, whereas our frequency-domain criterion remains robust under both short- and long-memory behaviour. Monte Carlo simulations and an empirical application to the UK Great Ratios support our theoretical findings.

Suggested Citation

  • Mustafa R. K{i}l{i}nc{c} & Michael Massmann, 2024. "Testing the order of fractional integration when smooth deterministic trends are possibly present," Papers 2410.10749, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2410.10749
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    References listed on IDEAS

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    1. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
    2. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
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