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# aarmam

## PURPOSE

Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean term)

## SYNOPSIS

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

## DESCRIPTION

``` Estimating Adaptive AutoRegressive-Moving-Average-and-mean model (includes mean term)

~~ This function is obsolete and is replaced by AMARMA

[z,E,REV,ESU,V,Z,SPUR] = aarmam(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)) + m(t) + e(t) + sum_i(b_i(t)*e(t-i))

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 = [m(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    determines the type of algorithm

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.

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

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

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