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Unit Roots and Asymmetric Smooth Transitions
Author(s) -
Sollis Robert,
Leybourne Stephen,
Newbold Paul
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00165
Subject(s) - mathematics , asymmetry , set (abstract data type) , phase transition , point (geometry) , transition (genetics) , unit root , function (biology) , statistical physics , econometrics , geometry , computer science , thermodynamics , physics , biochemistry , chemistry , quantum mechanics , evolutionary biology , biology , gene , programming language
It has been found useful, as an alternative to a difference‐stationary generating model, to consider the possibility of stationarity around a function that permits a smooth transition from one linear trend to another. Previous research has concentrated on functions that are symmetric around the point at which 50% of the transition is completed. Here we permit the possibility of asymmetry in the transition, allowing for example slow entry to and rapid exit from this evolutionary phase. It is shown through simulation and an interesting real data set that this can lead to the detection of further departures from difference stationarity.