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amarma

PURPOSE ^

Adaptive Mean-AutoRegressive-Moving-Average model estimation

SYNOPSIS ^

function [z,e,REV,ESU,V,Z,SPUR] = amarma(y, Mode, MOP, UC, z0, Z0, V0, W);

DESCRIPTION ^

 Adaptive Mean-AutoRegressive-Moving-Average model estimation
 [z,E,ESU,REV,V,Z,SPUR] = amarma(y, mode, MOP, UC, z0, Z0, V0, W); 
 Estimates AAR parameters with Kalman filter algorithm
     y(t) = sum_i(a(i,t)*y(t-i)) + mu(t) + E(t)

 State space model:
    z(t)=G*z(t-1) + w(t)      w(t)=N(0,W) 
    y(t)=H*z(t)   + v(t)      v(t)=N(0,V)    

 G = I, 
 z = [�(t)/(1-sum_i(a(i,t))),a_1(t-1),..,a_p(t-p),b_1(t-1),...,b_q(t-q)];
 H = [1,y(t-1),..,y(t-p),e(t-1),...,e(t-q)];
 W = E{(z(t)-G*z(t-1))*(z(t)-G*z(t-1))'}
 V = E{(y(t)-H*z(t-1))*(y(t)-H*z(t-1))'}

 Input:
       y    Signal (AR-Process)
       Mode
        [0,0] uses V0 and W  

       MOP     Model order [m,p,q], default [0,10,0] 
            m=1 includes the mean term, m=0 does not. 
            p and q must be positive integers
            it is recommended to set q=0. 
    UC    Update Coefficient, default 0
    z0    Initial state vector
    Z0    Initial Covariance matrix
      
 Output:
    z    AR-Parameter
    E    error process (Adaptively filtered process)
       REV     relative error variance MSE/MSY


 see also: AAR

 REFERENCE(S):
 [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications.
     ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany.
 [2] Schl�l A, Lee FY, Bischof H, Pfurtscheller G
     Characterization of Four-Class Motor Imagery EEG Data for the BCI-Competition 2005.
     Journal of neural engineering 2 (2005) 4, S. L14-L22

 More references can be found at
     http://www.dpmi.tu-graz.ac.at/~schloegl/publications/

CROSS-REFERENCE INFORMATION ^

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