NbbTools > Class library guide
We use the following definition for UCARIMA models:
where the 
are
independent. ARIMA processes
They also can be time polynomials, which can be considered as degenerated
ARIMA models
(
),
provided that at least one component has a stochastic behaviour.
The state space representation of an UCARIMA model can be directly derived from the state space representation of each of its components. More specifically, if the model contains n components, it will be defined by the following equations:
The matrices of the model are
where all the sub-matrices have been defined for the ARIMA state space representation.
(1-B)² (1-0.5B)y=(1-B)²e.
y=t + z, with
(1-B)²t=0
(1-0.5B)z=e
(y= first order auto-regressive model with trend).
The UCARIMA system matrices are:
That system can easily compared to the more usual state-space representation of regression model, that includes the coefficients of the regression in the state vector. In that case, we have:
