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

Ghassen Montasser

doi:10.3390/econometrics3020339

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.

Highlights

Kwiatkowski et al (KPSS) [1] have proposed an LM test with a null hypothesis such that a series is level or trend stationary and these authors assigned the limit theory under the null
The results indicated that the seasonal KPSS test preserved its good size and power properties
These findings show that the generalization of the asymptotic results of the standard KPSS test should not be performed in an automatic way, but rather, it is advisable to conduct careful analysis to establish equivalent results for the seasonal KPSS test

Summary

Introduction

Kwiatkowski et al (KPSS) [1] have proposed an LM test with a null hypothesis such that a series is level or trend stationary and these authors assigned the limit theory under the null. The KPSS test is widely used in empirical studies to examine trend stationarity This test is used as a complement to the standard unit root tests in analyzing time series properties. The purpose of this paper is to overcome this limitation To this end, other observational frequencies are considered in this study by examining monthly data. The effect of the presence of a linear trend on the seasonal KPSS test in finite samples for quarterly and monthly data is considered.

Preliminaries on the Seasonal KPSS Test

The Monte Carlo Analysis

Application

Conclusions

Methods