Time series: theory and methods
Time series: theory and methods
The statistical theory of linear systems
The statistical theory of linear systems
Identification of refined ARMA echelon form models for multivariate time series
Journal of Multivariate Analysis
Information science: Properties of infinite covariance matrices and stability of optimum predictors
Information Sciences: an International Journal
An efficient and versatile algorithm for computing the covariancefunction of an ARMA process
IEEE Transactions on Signal Processing
Evaluation of likelihood functions for Gaussian signals
IEEE Transactions on Information Theory
Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes (Corresp.)
IEEE Transactions on Information Theory
Evaluating exact VARMA likelihood and its gradient when data are incomplete
ACM Transactions on Mathematical Software (TOMS)
Original article: From general state-space to VARMAX models
Mathematics and Computers in Simulation
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The exact likelihood function of a Gaussian vector autoregressive-moving average (VARMA) model is evaluated in two nonstandard cases: (a) a parsimonious structured form, such as obtained in the echelon form structure or the scalar component model (SCM) structure; (b) a partially nonstationary (integrated of order 1) model in error-correction form. The starting point is any algorithm for computing the exact likelihood of a Gaussian VARMA time series. Our algorithm also provides the parameter estimates and their standard errors. The small sample properties of our algorithm were studied by Monte Carlo methods. Examples with real data are provided. models. Our algorithm also provides the parameter estimates and their standard errors. The small sample properties of our algorithm were studied by Monte Carlo methods. Examples with real data are provided.