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Unit roots and smooth transitions

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  • Stephen Leybourne
  • Paul Newbold
  • Dimitrios Vougas

Abstract

It is common practice in time series econometrics to test the null hypothesis that the generating function is integrated—i.e. that a series is stationary only after differencing—against the alternative of stationarity about either a fixed mean or a linear trend. However, there has been considerable recent interest in the possibility of stationarity around a linear trend with an abrupt break. Here we broaden this class of alternatives to allow for a smooth transition from one trend function to another. Dickey–Fuller type tests against this alternative are developed, and their properties are explored.

Suggested Citation

  • Stephen Leybourne & Paul Newbold & Dimitrios Vougas, 1998. "Unit roots and smooth transitions," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 83-97, January.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:1:p:83-97
    DOI: 10.1111/1467-9892.00078
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