Premium
SOME ASYMPTOTIC PROPERTIES OF THE SAMPLE COVARIANCES OF GAUSSIAN AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES
Author(s) -
Porat Boaz
Publication year - 1987
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.1467-9892.1987.tb00433.x
Subject(s) - mathematics , autoregressive model , autoregressive–moving average model , sample mean and sample covariance , asymptotic analysis , covariance , gaussian , covariance matrix , sample (material) , statistics , physics , quantum mechanics , estimator , chemistry , chromatography
. The paper deals with the asymptotic variances of the sample covariances of autoregressive moving average processes. Using state‐space representations and some matrix Lyapunov equation theory, closed‐form expressions are derived for the asymptotic variances of the sample covariances and for the Cramer‐Rao bounds on the process covariances. The main results obtained from these expressions are as follows: For ARMA ( p, q ) processes with p ≥ q , the sample covariance of order n is asymptotically efficient if and only if 0 ≤ n ≤ p – q . For ARMA ( p, q ) processes with p < q , none of the sample covariances is asymptotically efficient.