Optimal Estimation of Multivariate ARMA Models

A central problem in applied data analysis is time series In this paper, we develop a tractable approach to maximum modeling--estimating and forecasting a discrete-time likelihood parameter estimation for stochastic multivariate stochastic process--for which the autoregressive moving ARMA models. To efficiently compute a globally average (ARMA) and stochastic ARMA (Thiesson et al. optimal estimate, the problem is re-expressed as a regularized 2012) are fundamental models. An ARMA model describes loss minimization, which then allows recent algorithmic the behavior of a linear dynamical system under advances in sparse estimation to be applied (Shah et al. latent Gaussian perturbations (Brockwell and Davis 2002; 2012; Candes et al. 2011; Bach, Mairal, and Ponce 2008; Lütkepohl 2007), which affords intuitive modeling capability, Zhang et al. 2011; White et al. 2012). Although there has efficient forecasting algorithms, and a close relationship been recent progress in global estimation for ARMA, such to linear Gaussian state-space models (Katayama 2006, approaches have either been restricted to single-input singleoutput pp.5-6).