Testing for boundary conditions in case of fractionally integrated processes

Bounded integrated time series are a recent development of the time series literature. In this paper, we work on testing the presence of unknown boundaries with particular attention to the class of fractionally integrated time series. We firstly show, via a preliminaryMonteCarlo experiment, the effects of neglected boundaries conditions on the most commonly used estimators of the long memory parameter. Then, we develop a sieve bootstrap test to distinguish between unbounded and bounded fractionally integrated time series. We assess the finite sample performance of our test with a Monte Carlo experiment and apply it to the data set of the time series of the Danish Krone/Euro exchange rate.