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IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY

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 become an important modeling tool over the last two decades, are obtained by applying the fractional filter to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weights bn decay at the rate nd−1 and are not absolutely summable for long memory models (d > 0). It has been believed that this rate is inherited by the impulse responses of any long memory fractionally integrated model. We show that this conjecture does not hold in such generality, and we establish a simple necessary and sufficient condition for the rate nd−1 to be inherited by fractionally integrated processes.

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 NSF grants DMS-0804165 and DMS-0931948 at Utah State University. We thank Stanley Williams for suggesting Example 2.1. We thank three referees and Professor P.C.B. Phillips for comments that led to substantive improvements of our results and Professor Giuseppe Cavaliere for efficiently handling this submission.

References

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