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