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Impulse Responses Of Fractionally Integrated Processes With Long Memory

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  • Hassler, Uwe
  • Kokoszka, Piotr

Abstract

Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter null to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weights b decay at the rate n −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 n −1 to be inherited by fractionally integrated processes.

Suggested Citation

  • Hassler, Uwe & Kokoszka, Piotr, 2010. "Impulse Responses Of Fractionally Integrated Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1855-1861, December.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:06:p:1855-1861_00
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    Citations

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    Cited by:

    1. Uwe Hassler & Barbara Meller, 2014. "Detecting multiple breaks in long memory the case of U.S. inflation," Empirical Economics, Springer, vol. 46(2), pages 653-680, March.
    2. Psaradakis, Zacharias & Vávra, Marián, 2017. "A distance test of normality for a wide class of stationary processes," Econometrics and Statistics, Elsevier, vol. 2(C), pages 50-60.
    3. Hassler, Uwe & Hosseinkouchack, Mehdi, 2014. "Effect of the order of fractional integration on impulse responses," Economics Letters, Elsevier, vol. 125(2), pages 311-314.
    4. Hassler, Uwe & Rodrigues, Paulo M.M. & Rubia, Antonio, 2014. "Persistence in the banking industry: Fractional integration and breaks in memory," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 95-112.
    5. Al-Shboul, Mohammad & Anwar, Sajid, 2016. "Fractional integration in daily stock market indices at Jordan's Amman stock exchange," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 16-37.
    6. Hassler, Uwe, 2012. "Impulse responses of antipersistent processes," Economics Letters, Elsevier, vol. 116(3), pages 454-456.
    7. repec:spr:empeco:v:54:y:2018:i:4:d:10.1007_s00181-017-1276-8 is not listed on IDEAS
    8. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    9. Javier Contreras-Reyes & Wilfredo Palma, 2013. "Statistical analysis of autoregressive fractionally integrated moving average models in R," Computational Statistics, Springer, vol. 28(5), pages 2309-2331, October.

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