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

Mustafa R. K{\i}l{\i}n\c{c} and Michael Massmann

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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.

Date: 2024-10, Revised 2026-03
New Economics Papers: this item is included in nep-ecm and nep-ets
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