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 This function is obsolete and is replaced by AMARMA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://pub.ist.ac.at/~schloegl/publications/
Package: tsa