TY - JOUR
T1 - Time varying autoregressive moving average models for covariance estimation
AU - Wiesel, Ami
AU - Bibi, Ofir
AU - Globerson, Amir
PY - 2013
Y1 - 2013
N2 - We consider large scale covariance estimation using a small number of samples in applications where there is a natural ordering between the random variables. The two classical approaches to this problem rely on banded covariance and banded inverse covariance structures, corresponding to time varying moving average (MA) and autoregressive (AR) models, respectively. Motivated by this analogy to spectral estimation and the well known modeling power of autoregressive moving average (ARMA) processes, we propose a novel time varying ARMA covariance structure. Similarly to known results in the context of AR and MA, we address the completion of an ARMA covariance matrix from its main band, and its estimation based on random samples. Finally, we examine the advantages of our proposed methods using numerical experiments.
AB - We consider large scale covariance estimation using a small number of samples in applications where there is a natural ordering between the random variables. The two classical approaches to this problem rely on banded covariance and banded inverse covariance structures, corresponding to time varying moving average (MA) and autoregressive (AR) models, respectively. Motivated by this analogy to spectral estimation and the well known modeling power of autoregressive moving average (ARMA) processes, we propose a novel time varying ARMA covariance structure. Similarly to known results in the context of AR and MA, we address the completion of an ARMA covariance matrix from its main band, and its estimation based on random samples. Finally, we examine the advantages of our proposed methods using numerical experiments.
KW - Autoregressive moving average
KW - covariance estimation
KW - instrumental variables
KW - matrix completion
UR - http://www.scopus.com/inward/record.url?scp=84877919329&partnerID=8YFLogxK
U2 - 10.1109/TSP.2013.2256900
DO - 10.1109/TSP.2013.2256900
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84877919329
SN - 1053-587X
VL - 61
SP - 2791
EP - 2801
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 11
M1 - 6494326
ER -