A. Negiz et A. Cinar, PLS, BALANCED, AND CANONICAL VARIATE REALIZATION TECHNIQUES FOR IDENTIFYING VARMA MODELS IN STATE-SPACE, Chemometrics and intelligent laboratory systems, 38(2), 1997, pp. 209-221
This paper demonstrates the application of PLS regression, balanced re
alization, and canonical variate (CV) state space modeling techniques
in identifying stationary vector autoregressive moving average (VARMA)
type of time series models in state space. An example VARMA process m
odel is used to generate data, carry out modeling activities, and comp
are the three model development techniques. All realization methods pr
ovide equivalent state space models. Balanced realization can not hand
le singularities in the covariance matrix of past observations while a
ll other methods can accommodate such singularities. Balanced realizat
ion and classical PLS do not provide minimal state variables that are
orthogonal. 'Orthogonal states' PLS and canonical variate state space
realization give orthogonal state variables that provide robust parame
ter estimates from real data, however the PLS method requires an addit
ional singular value decomposition step.