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A Range Unit Root Test

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Author Info
Felipe M. Aparicio ()
Alvaro Escribano
Ana García

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Abstract

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of“long-wave” patterns observed not only in unit root time series but also in series following more complex data generating mechanisms. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties, among which its error-model-free asymptotic distribution, the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series and is asymptotically immune to noise.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws041104.

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Date of creation: Feb 2004
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Handle: RePEc:cte:wsrepe:ws041104

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References listed on IDEAS
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  3. repec:cup:etheor:v:11:y:1995:i:2:p:331-46 is not listed on IDEAS
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  6. Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers 359, Princeton, Department of Economics - Econometric Research Program.
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  18. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-70, October.
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  22. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October. [Downloadable!] (restricted)
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  24. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173. [Downloadable!] (restricted)
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  1. Felipe M. Aparicio & Alvaro Escribano, 2003. "Cointegration Tests Based On Record Counting Statistics," Statistics and Econometrics Working Papers ws036615, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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