Deciding whether a time series that appears nonstationary is in fact fractionally integrated or subject to structural change is a diffcult task. However, various tests have recently been introduced for distinguishing long memory from level shifts and nonlinearity. In this paper, three testing approaches based on the properties of semiparametric estimators of the fractional differencing parameter, d, are described and applied to the (log) Ireland-United Kingdom and Ireland-Germany real exchange rates. The two exchange rates behave quite differently over time and the new tests give different results for each; but overall the results provide fairly strong support for the possibility of nonlinearity rather than long memory.
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