Closure of Linear Processes

Journal of Theoretical Probability

Volumn 10, Issue 2, 1997, Pages 445-479

  Bickel, Peter J ^a   Bühlmann, Peter ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

AR process; Distinction from nonlinear process; Infinitely divisible law; MA process

Indexed keywords

EID: 0042941281     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022616601841     Document Type: Article

References (15)

1. Akamanam, S. I., Rao, M. Bhaskara, and Subramanyam, K. (1986). On the ergodicity of bilinear time series models. J. Time Series Anal. 7, 157-163.
2. Bickel, P. J., and Bühlmann, P. (1996). What is a linear process. Proc. Nat. Acad. Sci. 93, 12128-12131.
3. Bickel, P. J., and Freedman, D. A. (1981). Some asymptotic theory for the bootstrap. Ann. Stat. 9, 1196-1217.
4. Dunford, N., and Schwartz, J. T. (1957). Linear Operators. Part I: General Theory. Interscience Publishers, New York.
5. Durrett, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks/Cole, Pacific Grove.
6. Gorodetskii, V. V. (1977). On the strong mixing property for linear sequences. Theory Prob. Appl. 22, 411-413.
7. Grenander, U., and Szegö, G. (1984). Toeplitz Forms and their Applications. Second Edition, Chelsea, New York.
8. Hannan, E. J. (1987). Rational transfer function approximation. Stat. Sci. 5, 105-138.
9. Hartigan, J. A. (1983). Bayes Theory. Springer, New York.
10. Kleiner, B., Martin, R. D., and Thomson, D. J. (1979). Robust estimation of power spectra. J. Roy. Stat. Soc. B 41, 313-351.
11. Linnik, Y. V. (1964). Decomposition of Probability Distributions. Oliver and Boyd, Edinburgh.
12. Mallows, C. L. (1972). A note on asymptotic joint normality. Ann. Math. Stat. 43, 508-515.
13. Markushevich, A. I. (1977). Theory of Functions of a Complex Variable. Second Edition, Translated by R. A. Silverman. Chelsea, New York.
14. Subba Rao, T., and Gabr, M. M. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models. Lect. Notes in Stat. Vol. 24. Springer, Heidelberg.
15. Takano, K. (1956). Multidimensional central limit criterion in the case of bounded variances. Ann. Inst. Stat. Math. 7, 81-93.