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
On consistent testing for serial correlation of unknown form in vector time series models
Journal of Multivariate Analysis
HAC estimation and strong linearity testing in weak ARMA models
Journal of Multivariate Analysis
New Introduction to Multiple Time Series Analysis
New Introduction to Multiple Time Series Analysis
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The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. Relaxing the martingale difference assumption on the errors considerably extends the range of application of the VARMA models, and allows one to cover linear representations of general nonlinear processes. Conditions are given for the asymptotic normality of the QMLE. Particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework.