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# amarma

## 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

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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