MVAR estimates parameters of the Multi-Variate AutoRegressive model 

    Y(t) = Y(t-1) * A1 + ... + Y(t-p) * Ap + X(t);  
 whereas
    Y(t) is a row vecter with M elements Y(t) = y(t,1:M) 

 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);
 
 with 
       AR = [A1, ..., Ap];

 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 variances for increasing model order
	   PE(:,p*M+[1:M]) is the residual variance for model order p

 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:  buggy: Partial Correlation Estimation: Nutall-Strand [2] (biased correlation function)
  9:  Partial Correlation Estimation: Nutall-Strand [2] (biased correlation function)
  7:  Partial Correlation Estimation: Nutall-Strand [2] (unbiased correlation function)
  8:  Least Squares w/o nans in Y(t):Y(t-p)
 10:  ARFIT [3] 
 11:  BURGV [4] 
 13:  modified BURGV -  
 14:  modified BURGV [4] 
 15:  Least Squares based on correlation matrix
 22: Modified Partial Correlation Estimation: Vieira-Morf [2,5] using unbiased covariance estimates.
 25: Modified Partial Correlation Estimation: Vieira-Morf [2,5] using biased covariance estimates.

 90,91,96: Experimental versions 

    Imputation methods:
  100+Mode: 
  200+Mode: forward, past missing values are assumed zero
  300+Mode: backward, past missing values are assumed zero
  400+Mode: forward+backward, past missing values are assumed zero
 1200+Mode: forward, past missing values are replaced with predicted value
 1300+Mode: backward, 'past' missing values are replaced with predicted value
 1400+Mode: forward+backward, 'past' missing values are replaced with predicted value
 2200+Mode: forward, past missing values are replaced with predicted value + noise to prevent decaying
 2300+Mode: backward, past missing values are replaced with predicted value + noise to prevent decaying
 2400+Mode: forward+backward, past missing values are replaced with predicted value + noise to prevent decaying

Package: tsa