an:04041108
Zbl 0638.62091
Hannan, E. J.
Rational transfer function approximation (with discussion)
EN
Stat. Sci. 2, 135-161 (1987).
0883-4237 2168-8745
1987
j
62M10
autoregressive-moving average; rational transfer function; Kronecker indices; Kalman filter; McMillan degree; Hankel norm approximation; canonical correlation; balanced realization; minimum description length; Levinson-Whittle recursion; lattice algorithms; forgetting; Givens transformations; approximation of time series; order determination; general n-dimensional stationary time series; n-dimensional ARMA process; linear systems; infinite, block Hankel matrix; AIC; BIC; real time calculations
The paper is devoted to the problem how to approximate a general n- dimensional stationary time series by an n-dimensional ARMA process. The author discusses general features of linear systems and their description by an infinite, block Hankel matrix. He considers criteria for choosing orders of the ARMA process, especially AIC and BIC, and describes their properties.
Some algorithms are also introduced. They concern mainly real time calculations of the estimates. The comments written by Bhansali, Brillinger, Dahlhaus, Rissanen, Shibata and Solo contain some additional information and reflect views of their authors on specific problems discussed in the paper.
J.AndÄ›l