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SUFFICIENT STATISTICS FOR STATIONARY DISCRETE‐TIME GAUSSIAN RANDOM PROCESSES
Author(s) -
Dickinson Bradley W.
Publication year - 1982
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1982.tb00338.x
Subject(s) - mathematics , autoregressive model , gaussian , statistic , stationary process , statistics , dimension (graph theory) , gaussian process , star model , discrete time and continuous time , autoregressive integrated moving average , combinatorics , time series , physics , quantum mechanics
. It is known that the distribution of N samples of a stationary Gaussian autoregressive process admits a sufficient statistic whose dimension is independent of N . We show that this property depends not on the absence of spectral zeros in autoregressive models, but rather on the fact that the class of models has a fixed set of spectral zeros.