Fluctuation Tests for a Change in Persistence*
提出一组新的持久性变化检验，基于子样本的递归估计和重标极差波动统计量，用于检验时间序列是否从趋势平稳变为差分平稳或反之，并应用于美国通胀率数据。
Abstract 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.