Unit roots and smooth transitions

Stephen Leybourne (), Paul Newbold and Dimitrios Vougas

Journal of Time Series Analysis, 1998, vol. 19, issue 1, 83-97

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.

Date: 1998
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