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Firstly, the Source Information Flow Toolbox (SIFT) [27] in the EEGLAB was used to identify the optimal multivariate autoregressive model.
A multivariate autoregressive model is presented, and its parameters are estimated by least squares via the implementation of QR factorization.
multiple window time frequency analysis (MW-TFA) [9], frequency-dependant correlation coefficient [10], time varying causal coherence function (TVCCF) based on the multivariate autoregressive model [11].
In order to obtain these conditional probabilities, a multivariate autoregressive model with lag one [AR(1)] is chosen for extending multiple duration rainfall series.
The three main approaches are (1) multiple window time frequency analysis (MW-TFA) [9], (2) frequency-dependant correlation coefficient [10], (3) time varying causal coherence function (TVCCF) based on the multivariate autoregressive model [11]. .
Fin and rudder multivariate hybrid control system were designed using multivariate autoregressive model with multi-input (yaw and roll motion) and multi-output (rudder and fin angle), named MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System).
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They also build multivariate autoregressive models for a smaller number of links.
Causal coherence[40 42] or partial directed coherence[43, 44], based on multivariate autoregressive modeling may be used for this purpose.
Granger causality has been increasingly used to identify causal influence between time series based on multivariate autoregressive models.
The VAR processes are a generalization of multivariate autoregressive models (AR), where each variable is regressed on a set of others with several lags (Hamilton 1994; Enders 2009).
This paper describes a family of enhanced multivariate autoregressive models that can be used in SHM-oriented identification procedures and the implementation of a new advanced SHM system in the tower of the Engineering School of Bologna University.
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