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

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Abstract

Let {Xn:n∈Z} be a fractional ARIMA(p,d,q) process with partial autocorrelation function α(·). 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<1/2.

MSC

primary 62M10
60G10

Keywords

Partial autocorrelation function
Fractional ARIMA process
Stationary process
Long memory
Prediction error

Cited by (0)

1

Current address: University of Tokyo, Tokyo, Japan.