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Econometrics 2015, 3(2), 339-354; doi:10.3390/econometrics3020339

The Seasonal KPSS Test: Examining Possible Applications with Monthly Data and Additional Deterministic Terms

Department of Quantitative Methods, École Supérieure de Commerce de Tunis, University of Manouba, 2010 Manouba, Tunisia
Academic Editor: Kerry Patterson
Received: 13 January 2015 / Revised: 21 March 2015 / Accepted: 30 April 2015 / Published: 13 May 2015
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Abstract

The literature has been notably less definitive in distinguishing between finite sample studies of seasonal stationarity than in seasonal unit root tests. Although the use of seasonal stationarity and unit root tests is advised to determine correctly the most appropriate form of the trend in a seasonal time series, such a use is rarely noted in the relevant studies on this topic. Recently, the seasonal KPSS test, with a null hypothesis of no seasonal unit roots, and based on quarterly data, has been introduced in the literature. The asymptotic theory of the seasonal KPSS test depends on whether data have been filtered by a preliminary regression. More specifically, one may proceed to extracting deterministic components, such as the mean and trend, from the data before testing. In this paper, we examine the effects of de-trending on the properties of the seasonal KPSS test in finite samples. A sketch of the test’s limit theory is subsequently provided. Moreover, a Monte Carlo study is conducted to analyze the behavior of the test for a monthly time series. The focus on this time-frequency is significant because, as we mentioned above, it was introduced for quarterly data. Overall, the results indicated that the seasonal KPSS test preserved its good size and power properties. Furthermore, our results corroborate those reported elsewhere in the literature for conventional stationarity tests. These subsequent results assumed that the nonparametric corrections of residual variances may lead to better in-sample properties of the seasonal KPSS test. Next, the seasonal KPSS test is applied to a monthly series of the United States (US) consumer price index. We were able to identify a number of seasonal unit roots in this time series. [1] [1] Table 1 in this paper is copyrighted and initially published by JMASM in 2012, Volume 11, Issue 1, pp. 69–77, ISSN: 1538–9472, JMASM Inc., PO Box 48023, Oak Park, MI 48237, USA, ea@jmasm.com. View Full-Text
Keywords: KPSS test; deterministic seasonality; Brownian motion; LM test KPSS test; deterministic seasonality; Brownian motion; LM test
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Montasser, G.E. The Seasonal KPSS Test: Examining Possible Applications with Monthly Data and Additional Deterministic Terms. Econometrics 2015, 3, 339-354.

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