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

  • Authors:

  • Akihiko Inoue;Yukio Kasahara

  • Affiliations:

  • Hokkaido University, Sapporo, Japan;University of Tokyo, Tokyo, Japan and Hokkaido University, Sapporo, Japan

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2004

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Abstract

Let {Xn: n ∈ Z} be a fractional ARIMA(p, d, q) process with partial autocorrelation function α(ċ). In this paper, we prove that if d ∈ (-1/2,0) then |α(n)| ∼ |d|/n as n → ∞ This extends the previous result for the case 0 d