Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes

Annals of Applied Probability

Volumn 12, Issue 4, 2002, Pages 1471-1491

  Inoue, Akihiko ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Asymptotic behavior; Fractional ARIMA process; Partial autocorrelation function

Indexed keywords

EID: 0036441061     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1037125870     Document Type: Article

References (13)

1. BERAN, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York.
2. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1989). Regular Variation, 2nd ed. Cambridge Univ. Press.
3. BROCKWELL, P. J. AND DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
4. GRANGER, C. W. AND JOYEUX, R. (1980). An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1 15-29.
5. HOSKING, J. R. M. (1981). Fractional differencing. Biometrika 68 165-176.
6. INOUE, A. (1997). Regularly varying correlation functions and KMO-Langevin equations. Hokkaido Math. J. 26 1-26.
7. INOUE, A. (2000). Asymptotics for the partial autocorrelation function of a stationary process. J. Anal. Math. 81 65-109.
8. INOUE, A. and KASAHARA, Y. (1999). On the asymptotic behavior of the prediction error of a stationary process. In Trends in Probability and Related Analysis (N. Kono and N. R. Shieh, eds.) 207-218. World Scientific, Singapore.
9. INOUE, A. and KASAHARA, Y. (2000). Asymptotics for prediction errors of stationary processes with reflection positivity. J. Math. Anal. Appl. 250 299-319.
10. KOKOSZKA, P. S. and TAQQU, M. S. (1995). Fractional ARIMA with stable innovations. Stochastic Process. Appl. 60 19-47.
11. RAMSEY, F. L. (1974). Characterization of the partial autocorrelation function. Ann. Statist. 2 1296-1301.
12. ROZANOV, Y. A. (1967). Stationary Random Processes. Holden-Day, San Francisco.
13. RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York.