Robust Tests for Deterministic Seasonality and Seasonal Mean Shifts

Sam Astill and AM Robert Taylor

Essex Finance Centre Working Papers from University of Essex, Essex Business School

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.

Keywords: Seasonality; Seasonal Level Breaks; Seasonal Unit Roots; Robust Tests (search for similar items in EconPapers)
Date: 2018-01
New Economics Papers: this item is included in nep-ecm, nep-eff and nep-ets
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