Marcelo Reyes

Testing for a Unit Root in Variables with a Double Change in the Mean

In this paper, we obtain a statistic that is useful for the analysis of the integration order of a variable which exhibits two changes in its mean. Our work begins by showing that the most commonly used unit root tests behave asymptotically in a correct manner for double changing mean variables. However, their use is not advisable in finite samples; rather, is better to design a new statistic which takes into account the presence of the two level shifts. We calculate the asymptotic distribution of this new statistic and tabulate it for several sample sizes using Monte Carlo methods. This new statistic allows us to show that the USA and UK real interest rates can be considered as stationary variables with a double shift in their mean.

EFFECT OF A SHIFT IN THE TREND FUNCTION ON DICKEY FULLER UNIT ROOT TESTS

This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte Carlo exercises show that the argument of Perron (1989, Econometrica 57, 1361–1401) that the tests are biased in favor of nonrejection of the unit root hypothesis remains valid for sample sizes of practical interest.

The European Union currencies and the US dollar: from post-Bretton-Woods to the Euro

Abstract In this paper we study the evolution of the US dollar real exchange rate vis-a-vis the European Union currencies in the floating post-Bretton-Woods era, both before and after the birth of the Euro. In the first period we find that most of the persistence shown by this rate is due to the movements of the US dollar during the mid-1980s. Once these effects are isolated, we can conclude that the US dollar real exchange rate exhibits stationarity with those currencies that are closely linked to the German Mark. However, when we include the observations covering the period during which the Euro was created, we cannot reject the unit root null hypothesis for any currency.

The asymptotic behaviour of the Dickey-Fuller tests under the crash hypothesis

This paper considers the behaviour of the Dickey-Fuller tests when the variable being studied is generated according to Perrons (1989) crash hypothesis. We show that these statistics tend towards the Dickey-Fuller distributions under the null hypothesis and diverge towards -[infinity] under the alternative.

Structural breaks, unit roots and methods for removing the autocorrelation pattern

This paper examines the asymptotic and finite sample behaviour of the ADF and Phillips-Perron statistics under the presence of a break in the trend function. We prove that the break magnitude affects these two statistics in a similar way, drawing them closer the acceptance zone, the higher the break magnitude. By contrast, the influence of the lag truncation parameter does not have a similar effect on them, being very important for the ADF whilst negligible for the Phillips-Perron statistics.