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Robust Tests for Deterministic Seasonality and Seasonal Mean Shifts

Astill, S and Taylor, AMR (2018) 'Robust Tests for Deterministic Seasonality and Seasonal Mean Shifts.' The Econometrics Journal. ISSN 1368-4221

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Abstract

We develop tests for the presence of deterministic seasonal behaviour and seasonal mean shifts in a seasonally observed univariate time series. These tests are designed to be asymptotically robust to the order of integration of the series at both the zero and seasonal frequencies. Motivated by the approach of Hylleberg, Engle, Granger and Yoo [1990, Journal of Econometrics vol. 44, pp. 215-238], we base our approach on linear filters of the data which remove any potential unit roots at the frequencies not associated with the deterministic component(s) under test. Test statistics are constructed using the filtered data such that they have well defined limiting null distributions regardless of whether the data are either integrated or stationary at the frequency associated with the deterministic component(s) under test. In the same manner as Vogelsang [1998, Econometrica vol. 66, pp. 123-148], Bunzel and Vogelsang [2005, Journal of Business and Economic Statistics vol. 23, pp. 381-394] and Sayginsoy and Vogelsang [2011, Econometric Theory vol. 27, pp. 992-1025], we scale these statistics by a function of an auxiliary seasonal unit root statistic. This allows us to construct tests which are asymptotically robust to the order of integration of the data at both the zero and seasonal frequencies. Monte Carlo evidence suggests that our proposed tests have good finite sample size and power properties. An empirical application to U.K. GDP indicates the presence of seasonal mean shifts in the data.

Item Type: Article
Uncontrolled Keywords: Seasonality, Seasonal Level Breaks, Seasonal Unit Roots, Robust Tests
Subjects: H Social Sciences > HG Finance
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Elements
Date Deposited: 15 Feb 2018 11:06
Last Modified: 15 Feb 2018 11:08
URI: http://repository.essex.ac.uk/id/eprint/21265

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