Testing for boundary conditions in case of fractionally integrated processes

  • Margherita GerolimettoEmail author
  • Stefano Magrini
Original Paper


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 preliminary Monte Carlo 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.


Bounded fractionally integrated processes Range statistics Sieve bootstrap 

JEL Classifications

C1: Econometric and Statistical Methods: general 



We are very thankful to the Editor and two anonymous Referees for the helpful and constructive comments on a previous version of this paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsCa’Foscari University VeniceVeneziaItaly

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