PLS, BALANCED, AND CANONICAL VARIATE REALIZATION TECHNIQUES FOR IDENTIFYING VARMA MODELS IN STATE-SPACE

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.