Testing for Seasonal Unit Roots with Temporally Aggregated Time Series

Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415–442), Smith and Taylor (1998, Journal of Econometrics 85, 269–288; 1999, Journal of Time Series Analysis 20, 453–476; 1999, Discussion paper 99-15 in economics, University of Birmingham), and Taylor (1998, Journal of Time Series Analysis 19, 349–368) have developed a method of testing for seasonal unit roots of zero and nonzero frequencies. They propose to use t- and F-statistics as criteria that are obtained from an auxiliary regression and find their limiting distributions as the number of observations becomes large. Their limiting distributions are expressed by means of Brownian motions. In this paper the moment generating functions associated with the limiting distributions are derived, and it is shown, as in Nabeya (2000, Econometric Theory 16, 200–230), that the limiting distribution of t is well approximated by a distribution given in Gram–Charlier series. The limiting distribution of F is also well approximated by another type of distribution.

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Unit roots and seasonal unit roots in macroeconomic time series

Economics Letters ◽

10.1016/0165-1765(91)90143-9 ◽

1991 ◽

Vol 35 (3) ◽

pp. 273-277 ◽

Cited By ~ 23

Author(s):

Hahn Shik Lee ◽

Pierre L. Siklos

Keyword(s):

Time Series ◽

Unit Roots ◽

Seasonal Unit Roots ◽

Macroeconomic Time Series

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Using singular spectrum analysis for inference on seasonal time series with seasonal unit roots

International Journal of Computational Economics and Econometrics ◽

10.1504/ijcee.2020.107371 ◽

2020 ◽

Vol 10 (2) ◽

pp. 149 ◽

Cited By ~ 1

Author(s):

Dimitrios D. Thomakos ◽

Hossein Hassani

Keyword(s):

Time Series ◽

Spectrum Analysis ◽

Singular Spectrum Analysis ◽

Unit Roots ◽

Seasonal Unit Roots ◽

Singular Spectrum ◽

Seasonal Time Series

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Tests for seasonal unit roots in panels of cross-sectionally correlated time series

Statistics ◽

10.1080/02331880701600463 ◽

2009 ◽

Vol 43 (2) ◽

pp. 139-152 ◽

Cited By ~ 1

Author(s):

Dong Wan Shin ◽

Man-Suk Oh

Keyword(s):

Time Series ◽

Unit Roots ◽

Seasonal Unit Roots

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The Nature of Seasonality in Spanish Tourism Time Series

Tourism Economics ◽

10.5367/000000005775108764 ◽

2005 ◽

Vol 11 (4) ◽

pp. 483-499 ◽

Cited By ~ 23

Author(s):

J. Cunado ◽

L.A. Gil-Alana ◽

F. Péarez de Gracia

Keyword(s):

Time Series ◽

White Noise ◽

Unit Roots ◽

Testing Procedure ◽

Fractional Differentiation ◽

Integrated Models ◽

Seasonal Unit Roots ◽

Long Run ◽

Noise Disturbances ◽

Hotel Accommodation

This paper deals with the analysis of seasonality in the context of tourism time series. The authors present a general testing procedure that permits them to consider the cases of deterministic and/or stochastic (with integer and fractional differentiation) seasonality in a unified treatment. The procedure is applied to four Spanish tourism time series: the total (foreign and domestic) number of tourists, the number of domestic tourists, the number of nights spent in hotel accommodation by tourists, and the number of nights spent in hotel accommodation by domestic tourists. The results show that the series can be well described in terms of seasonally fractionally integrated models, with the orders of integration ranging between 0.4 and 0.6 in the case of white noise disturbances, and values slightly smaller with autocorrelated disturbances. Thus the standard practice of taking seasonal dummies (deterministic seasonality) or integer differentiation (seasonal unit roots) may lead to erroneous conclusions about the stochastic behaviour of the series. Moreover, the series seem to be mean reverting, implying that shocks affecting them disappear in the long run though at a very slow hyperbolic rate.

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