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Fluctuation Tests for a Change in Persistence *
Author(s) -
Taylor A. M. Robert
Publication year - 2005
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/j.1468-0084.2004.00117.x
Subject(s) - mathematics , econometrics , null hypothesis , consistency (knowledge bases) , statistics , persistence (discontinuity) , inflation (cosmology) , statistical hypothesis testing , asymptotic analysis
In this paper, we develop a set of new persistence change tests which are similar in spirit to those of Kim [ Journal of Econometrics (2000) Vol. 95, pp. 97–116], Kim et al. [ Journal of Econometrics (2002) Vol. 109, pp. 389–392] and Busetti and Taylor [ Journal of Econometrics (2004) Vol. 123, pp. 33–66]. While the exisiting tests are based on ratios of sub‐sample Kwiatkowski et al. [ Journal of Econometrics (1992) Vol. 54, pp. 158–179]‐type statistics, our proposed tests are based on the corresponding functions of sub‐sample implementations of the well‐known maximal recursive‐estimates and re‐scaled range fluctuation statistics. Our statistics are used to test the null hypothesis that a time series displays constant trend stationarity [ I (0)] behaviour against the alternative of a change in persistence either from trend stationarity to difference stationarity [ I (1)], or vice versa. Representations for the limiting null distributions of the new statistics are derived and both finite‐sample and asymptotic critical values are provided. The consistency of the tests against persistence change processes is also demonstrated. Numerical evidence suggests that our proposed tests provide a useful complement to the extant persistence change tests. An application of the tests to US inflation rate data is provided.