论文信息 - ON TIME-REVERSIBILITY OF MULTIVARIATE LINEAR PROCESSES

ON TIME-REVERSIBILITY OF MULTIVARIATE LINEAR PROCESSES

We study the time-reversibility of multivariate linear processes, introduc- ing a necessary and sucien t condition related to linear transforms of the multivari- ate linear process. Conditions analogous to Cheng's for univariate non-Gaussian linear processes are also explored; these are in terms of the noise distribution and the model parameters. The exploration results in an easily veriable set of neces- sary and sucien t conditions for a multivariate non-Gaussian linear process driven by a univariate noise, leaving the case of multivariate noise as a challenging open problem.

Howell Tong | Zhiqiang Zhang

[1] Richard A. Davis,et al. TIME‐REVERSIBILITY, IDENTIFIABILITY AND INDEPENDENCE OF INNOVATIONS FOR STATIONARY TIME SERIES , 1992 .

[2] Q. Cheng. On the Unique Representation of Non-Gaussian Linear Processes , 1992 .

[3] Qiansheng Cheng. Miscellanea. On time-reversibility of linear processes , 1999 .

[4] Richard A. Davis,et al. Time Series: Theory and Methods (2nd ed.). , 1992 .

[5] G. Weiss. TIME-REVERSIBILITY OF LINEAR STOCHASTIC PROCESSES , 1975 .

[6] H. Tong,et al. An adaptive estimation of dimension reduction space, with discussion , 2002 .

[7] David F. Findley,et al. The uniqueness of moving average representations with independent and identically distributed random variables for non-Gaussian stationary time series , 1986 .

[8] P. Whittle. On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix , 1963 .

[9] E. J. Hannan,et al. Multiple time series , 1970 .

[10] Claude Lefèvre,et al. On time-reversibility and the uniqueness of moving average representations for non-Gaussian stationary time series , 1988 .

[11] Murray Rosenblatt,et al. Gaussian and Non-Gaussian Linear Time Series and Random Fields , 1999 .

[12] H. Tong,et al. An adaptive estimation of dimension reduction , 2002 .

[13] Dag Tjøstheim,et al. Modelling panels of intercorrelated autoregressive time series , 1999 .