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Testing for the Presence of a Random Walk in Series with Structural Breaks

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  • Fabio Busetti
  • Andrew Harvey

Abstract

We consider tests for the presence of a random walk component in a stationary or trend stationary time series and extend them to series that contain structural breaks. The locally best invariant (LBI) test is derived and the asymptotic distribution is obtained. Then a modified test statistic is proposed. The advantage of this statistic is that its asymptotic distribution is not dependent on the location of the break point and its form is that of the generalized Cramer–von Mises distribution, with degrees of freedom depending on the number of break points. The performance of this modified test is shown, via some simulation experiments, to be comparable with that of the LBI test. An unconditional test, based on the assumption that there is a single break at an unknown point, is also examined. The use of the tests is illustrated with data on the flow of the Nile and US gross national product.

Suggested Citation

  • Fabio Busetti & Andrew Harvey, 2001. "Testing for the Presence of a Random Walk in Series with Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 127-150, March.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:2:p:127-150
    DOI: 10.1111/1467-9892.00216
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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