Iacone, Fabrizio and Leybourne, Stephen J and Taylor, AM Robert (2019) Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point. Econometric Theory, 35 (6). pp. 1201-1233. DOI https://doi.org/10.1017/S0266466618000361
Iacone, Fabrizio and Leybourne, Stephen J and Taylor, AM Robert (2019) Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point. Econometric Theory, 35 (6). pp. 1201-1233. DOI https://doi.org/10.1017/S0266466618000361
Iacone, Fabrizio and Leybourne, Stephen J and Taylor, AM Robert (2019) Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point. Econometric Theory, 35 (6). pp. 1201-1233. DOI https://doi.org/10.1017/S0266466618000361
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 applied either to the levels or first differences of the data, depending on the value specified for the long memory parameter under the null hypothesis. 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, 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.
Item Type: | Article |
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Uncontrolled Keywords: | Fractional integration; trend break; Lagrange multiplier test; asymptotically locally most powerful test |
Subjects: | H Social Sciences > HG Finance |
Divisions: | Faculty of Social Sciences Faculty of Social Sciences > Essex Business School |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 23 Aug 2018 15:35 |
Last Modified: | 16 May 2024 19:32 |
URI: | http://repository.essex.ac.uk/id/eprint/22879 |
Available files
Filename: BakerStreetR2V2.pdf