Autoregressive identification of Kronecker graphical models

1 Graphical models of autoregressive processes

We consider the problem of fitting a Gaussian autoregressive model to a time series, subject to conditional independence constraints. This is an extension of the classical covariance selection problem to times series. The conditional independence constraints impose a sparsity pattern on the inverse of the spectral density matrix, and result in nonconvex quadratic equality constraints in the max...

Topology Selection in Graphical Models of Autoregressive Processes

An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series. The graph topology of the model represents the sparsity pattern of the inverse spectrum of the time series and characterizes conditional independence relations between the variables. The method proposed in the paper is based on an l1-type nonsmooth regularization of the conditional maxim...

Convergence Properties of Kronecker Graphical Lasso Algorithms

This report presents a thorough convergence analysis of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model. The KGlasso model, originally called the transposable regularized covariance model by Allen et al [1], implements a pair of `1 penalties on each Kronecker factor to enforce spar...

System Identification of Nonlinear Autoregressive Models in Monitoring Dengue Infection

This paper proposes system identification on application of nonlinear AR (NAR) based on Artificial Neural Network (ANN) for monitor of dengue infections. In building the model, three selection criteria, i.e. the final prediction error (FPE), Akaike’s Information Criteria (AIC), and Lipschitz number were used. Each of the models is divided into two approaches, which are unregularized approach an...

Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models