Explicit representation of finite predictor coefficients and its applications

Annals of Statistics

Volumn 34, Issue 2, 2006, Pages 973-993

  Inoue, Akihiko ^a   Kasahara, Yukio ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

AR coefficients; Baxter's inequality; Fractional ARIMA processes; Long memory; MA coefficients; Predictor

Indexed keywords

EID: 33746227394     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000209     Document Type: Article

References (27)

1. BAXTER, G. (1962). An asymptotic result for the finite predictor. Math. Scand. 10 137-144. MR0149584
2. BERAN, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York. MR1304490
3. BERK, K. N. (1974). Consistent autoregressive spectral estimates. Ann. Statist. 2 489-502. MR0421010
4. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1989). Regular Variation, 2nd ed. Cambridge Univ. Press. MR1015093
5. BLOOMFIELD, P., JEWELL, N. P. and HAYASHI, E. (1983). Characterizations of completely nondeterministic stochastic processes. Pacific J. Math. 107 307-317. MR0705750
6. BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York. MR1093459
7. CHENG, R. and POURAHMADI, M. (1993). Baxter's inequality and convergence of finite predictors of multivariate stochastic processes. Probab. Theory Related Fields 95 115-124. MR1207310
8. GINOVIAN, M. S. (1999). Asymptotic behavior of the prediction error for stationary random sequences. J. Contemp. Math. Anal. 34 18-36. MR1854056
9. GRANGER, C. W. J. and JOYEUX, R. (1980). An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1 15-29. MR0605572
10. GRENANDER, U. and SZEGÖ, G. (1958). Toeplitz Forms and Their Applications. Univ. California Press, Berkeley. MR0094840
11. HARDY, G. H., LITTLEWOOD, J. E. and PÓLYA, G. (1952). Inequalities, 2nd ed. Cambridge Univ. Press. MR0046395
12. HELSON, H. and SARASON, D. (1968). Past and future. Math. Scand. 21 5-16. MR0236989
13. HOSKING, J. R. M. (1981). Fractional differencing. Biometrika 68 165-176. MR0614953
14. INOUE, A. (1997). Regularly varying correlation functions and KMO-Langevin equations. Hokkaido Math. J. 26 457-482. MR1463098
15. INOUE, A. (2000). Asymptotics for the partial autocorrelation function of a stationary process. J. Anal. Math. 81 65-109. MR1785278
16. INOUE, A. (2001). What does the partial autocorrelation function look like for large lags? Preprint. Available at www.math.hokudai.ac.jp/~inoue/PT-01- 123.pdf.
17. INOUE, A. (2002). Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes. Ann. Appl. Probab. 12 1471-1491. MR1936600
18. INOUE, A. and KASAHARA, Y. (2004). Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing. J. Multivariate Anal. 89 135-147. MR2041213
19. KOKOSZKA, P. S. and TAQQU, M. S. (1995). Fractional ARIMA with stable innovations. Stochastic Process. Appl. 60 19-47. MR1362317
20. KOLMOGOROV, A. N. (1941). Stationary sequences in Hilbert space. Bull. Math. Univ. Moscow 2 1-40. (In Russian.) MR0009098
21. MAKAGON, A. and WERON, A. (1976). Wold-Cramér concordance theorems for interpolation of q-variate stationary processes over locally compact Abelian groups. J. Multivariate Anal. 6 123-137. MR0426126
22. POURAHMADI, M. (2001). Foundations of Time Series Analysis and Prediction Theory. Wiley, New York. MR1849562
23. ROZANOV, Y. A. (1967). Stationary Random Processes. Holden-Day, San Francisco. MR0214134
24. SALEHI, H. (1979). Algorithms for linear interpolator and interpolation error for minimal stationary stochastic processes. Ann. Probab. 7 840-846. MR0542133
25. SARASON, D. (1978). Function theory on the unit circle. Notes for lectures given at a Conference at Virginia Polytechnic Institute and State University, Blacksburg, VA. MR0521811
26. SIMON, B. (2005). Orthogonal Polynomials on the Unit Circle. Part 1. Classical Theory. Amer. Math. Soc., Providence, RI. MR2105088
27. SIMON, B. (2005). Orthogonal Polynomials on the Unit Circle. Part 2. Spectral Theory. Amer. Math. Soc., Providence, RI. MR2105089