PLS, balanced, and canonical variate realization techniques for identifying VARMA models in state space

Abstract

This paper demonstrates the application of PLS regression, balanced realization, 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 model is used to generate data, carry out modeling activities, and compare the three model development techniques. All realization methods provide equivalent state space models. Balanced realization can not handle singularities in the covariance matrix of past observations while all other methods can accommodate such singularities. Balanced realization 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 parameter estimates from real data, however the PLS method requires an additional singular value decomposition step.