Faculty of Economics and Business Administration Publications Database

Impulse Responses of Fractionally Integrated Processes with Long Memory

Kokoszka, Piotr
Volume: 26
Number: 6
Pages: 1855 - 1861
Month: December
ISSN-Print: 0266-4666
Link External Source: Online Version
Year: 2010
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.