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mvar

PURPOSE ^

MVAR estimates Multi-Variate AutoRegressive model parameters

SYNOPSIS ^

function [ARF,RCF,PE,DC,varargout] = mvar(Y, Pmax, Mode);

DESCRIPTION ^

 MVAR estimates Multi-Variate AutoRegressive model parameters
 Several estimation algorithms are implemented, all estimators 
 can handle data with missing values encoded as NaNs.  

     [AR,RC,PE] = mvar(Y, p);
     [AR,RC,PE] = mvar(Y, p, Mode);

 INPUT:
  Y     Multivariate data series 
  p     Model order
  Mode     determines estimation algorithm 

 OUTPUT:
  AR    multivariate autoregressive model parameter
  RC    reflection coefficients (= -PARCOR coefficients)
  PE    remaining error variance

 All input and output parameters are organized in columns, one column 
 corresponds to the parameters of one channel.

 Mode determines estimation algorithm. 
  1:  Correlation Function Estimation method using biased correlation function estimation method
           also called the 'multichannel Yule-Walker' [1,2] 
  6:  Correlation Function Estimation method using unbiased correlation function estimation method

  2:  Partial Correlation Estimation: Vieira-Morf [2] using unbiased covariance estimates.
               In [1] this mode was used and (incorrectly) denominated as Nutall-Strand. 
        Its the DEFAULT mode; according to [1] it provides the most accurate estimates.
  5:  Partial Correlation Estimation: Vieira-Morf [2] using biased covariance estimates.
        Yields similar results than Mode=2;

  3:  Partial Correlation Estimation: Nutall-Strand [2] (biased correlation function)
  7:  Partial Correlation Estimation: Nutall-Strand [2] (unbiased correlation function)

 10:  ARFIT [3] 
 11:  BURGV [4] 

 REFERENCES:
  [1] A. Schl\'ogl, Comparison of Multivariate Autoregressive Estimators.
       Signal processing, Elsevier B.V. (in press). 
       available at http://dx.doi.org/doi:10.1016/j.sigpro.2005.11.007
  [2] S.L. Marple 'Digital Spectral Analysis with Applications' Prentice Hall, 1987.
  [3] Schneider and Neumaier)
  [4] Stijn de Waele, 2003


 A multivariate inverse filter can be realized with 
   [AR,RC,PE] = mvar(Y,P);
   e = mvfilter([eye(size(AR,1)),-AR],eye(size(AR,1)),Y);
  
 see also: MVFILTER, MVFREQZ, COVM, SUMSKIPNAN, ARFIT2

CROSS-REFERENCE INFORMATION ^

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