Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 30

The second filter has the input e t , transfer function I ( B ), and output w t

I

1

B ,

w e

t t

and the third filter has the input w t , the transfer function s d ( i.e . it is a nonstationary
summation filter) and the output

x

d

x sw

t t

or

I

1
()

d

BB T .

x s a t t

Table 2.1 summarizes some features of AR, MA, and ARMA model.

2.5.5 CARMAX Model

In systems and control theory the CARMAC model is used for design of minimum
variance and predictive control (see Section 2.10.3). For deterministic dynamic
systems with an input signal u ( t ) and a disturbance e ( t ) the CARMA or CARMAX
model is defined as

A zyt ()() ()() ()()

1

Bzut

1

Czet

1

,

where

() n

1 i

A z ¦ a z 0 i 1

i

i 0

() m

1 j

Bz ¦ bz

j

j 1

p

1

cz Q
Q

Cz () ¦ 0 c . 1

Q 0

The acronym CARMAX stands control autoregressive moving-average model
with auxiliary inputs . This has analogy with the Kalman notation of a state-space
model of the filter.