Nonparametric Tests for Periodic Integration

Tomás del Barrio Castro 1  and Denise R Osborn 2
  • 1 University of the Balearic Islands
  • 2 University of Manchester

We propose two nonparametric methods to test the null hypothesis of periodic integration, one based on the variance ratio unit root test of Breitung (2002) and the other on the modified Sargan-Bhargava test developed by Stock (1999). The former does not require specification of short-run dynamics, while nevertheless delivering a pivotal limiting distribution; however, the latter requires estimation of the long-run variance. The asymptotic distributions of the new statistics are shown to be invariant to whether the process is periodically integrated or a conventional I(1) process, whereas tests based on the I(1) assumption are not. Further, the new tests do not require nonlinear estimation and can be implemented in a straightforward way. Monte Carlo results show that the variance ratio test has very good finite sample size, but the modified Sargan-Bhargava test has much better power, which can be comparable to that of the parametric likelihood ratio test. Finally, an empirical application illustrates the use of the tests through an analysis of six monthly component Industrial Production Indices for the U.S.

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The Journal of Time Series Econometrics (JTSE) serves as an internationally recognized outlet for important new research in both theoretical and applied classical and Bayesian time series, spatial and panel data econometrics. The scope of the journal includes papers dealing with estimation, testing and other methodological aspects involved in the application of time series and spatial analytic techniques to economic, financial and related data.

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