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On detection of unit roots generalizing the classic Dickey-Fuller approach

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  • Steland, Ansgar

Abstract

If we are given a time series of economic data, a basic question is whether the series is stationary or a random walk, i.e., has a unit root. Whereas the problem to test the unit root null hypothesis against the alternative of stationarity is well studied in the context of classic hypothesis testing in the sense of Neyman, sequential and monitoring approaches have not been studied in detail yet. We consider stopping rules based on a sequential version of the well known Dickey-Fuller test statistics in a setting, where the asymptotic distribution theory becomes a nice and simple application of weak convergence of Ito integrals. More sophisticated extensions studied elsewhere are outlined. Finally, we present a couple of simulations.

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  • Steland, Ansgar, 2005. "On detection of unit roots generalizing the classic Dickey-Fuller approach," Technical Reports 2005,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200509
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    1. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    2. Ansgar Steland, 2004. "Sequential control of time series by functionals of kernal-weighted empirical processes under local alternatives," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 229-249, November.
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