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

TL;DR

This paper develops a robust frequency-domain test for fractional integration in models with smooth deterministic trends, accommodating nonlinear processes and heteroskedasticity, with empirical validation on UK data.

Contribution

It introduces a novel frequency-domain Lagrange multiplier test and information criterion for the order of fractional integration with smooth trends, improving over traditional time-domain methods.

Findings

Frequency-domain criterion remains consistent under various conditions.

Monte Carlo simulations validate the test's accuracy.

Empirical application demonstrates practical usefulness.

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.