Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

Article, Research English OPEN
Inoue, Akihiko; Kasahara, Yukio;
(2004)
  • Publisher: Elsevier BV
  • Journal: Journal of Multivariate Analysis,volume 89,issue 1,pages135-147 (issn: 0047-259X)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1016/s0047-259x(02)00027-1
  • Subject: stationary process | Statistics, Probability and Uncertainty | Numerical Analysis | fractional ARIMA process | Statistics and Probability | long memory | prediction error | partial autocorrelation function

Let {Xn : ri E Z} be a fractional ARIMA{p, d, q) process with partial autocorrelation functiono:(·). In this paper, we prove that if d E ( 􀀙1/2, 0) then jo:(n)I rv jdj/n as n ---+ oo. This extends the previous result for the case O < d < 1/2.
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