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IMPULSE RESPONSES OF FRACTIONALLYINTEGRATED PROCESSES WITH LONGMEMORY

Published online by Cambridge University Press:  08 April 2010

Uwe Hassler  and
Piotr Kokoszka
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Abstract

Fractionally integrated time series, which have becomean important modeling tool over the last twodecades, are obtained by applying the fractionalfilter to a weaklydependent (short memory) sequence. Weakly dependentsequences are characterized by absolutely summableimpulse response coefficients of their Woldrepresentation. The weightsbn decay at the ratend−1 andare not absolutely summable for long memory models(d > 0). It has been believedthat this rate is inherited by the impulse responsesof any long memory fractionally integrated model. Weshow that this conjecture does not hold in suchgenerality, and we establish a simple necessary andsufficient condition for the ratend−1 to beinherited by fractionally integrated processes.

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Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1855 - 1861
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

This research was partially supported by NSFgrants DMS-0804165 and DMS-0931948 at Utah StateUniversity. We thank Stanley Williams forsuggesting Example 2.1. We thank three refereesand Professor P.C.B. Phillips for comments thatled to substantive improvements of our results andProfessor Giuseppe Cavaliere for efficientlyhandling this submission.

References

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