Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

2.2. LINEAR PROCESS 9
In the z-domain the model becomes
X(z) = G(z)E(z) (2.4)
where G(z) is the transfer function, and E(z) is the z-transform of the white noise
process (innovations).
The transfer function G(z) can be approximated by rational function in the
z−transform domain:
I can rewrite the equation (2.4) as follows
G(z) = B(z)
. (2.5)
A(z)
X(z) = B(z)
E(z) . (2.6)
A(z)
The latter, when mapped back to time, is represented as follows:
p
q
xn + aixn−i = εn + biεn−i . (2.7)
i=1
i=1
When all the coefficients bi = 0 the last expression is often called an autoregressive
model of order p, AR(p) (Box and Jenkins, 1970; Makhoul, 1975; Chatfield, 1989).
Otherwise, when all ai = 0 then the model called a Moving Average (MA) model.
The developed algorithm is written in MATLAB.
Linear prediction models for time series modeling use linear autoregressive mod-
els. Figure 2.1 represents the infinite impulse response (IIR) of an AR model.