We are interested in identifying variables which do not form part of a model, but whose influence on the output is evidenced by anomalous behaviour of the model.
This may be the result of premature dimension reduction or principal axis determination, both of which are essential steps in the analysis of commercial data whose dimensionality is too high to allow of a solution which encompasses all identified variables.
The anomalies we seek are of the following types:
- Non-linear deviations from predicted values
- Unexplained bifurcations
By extending the state space to accommodate exogenous variables, we allow VARMAX exploration of principal components in longitudinal studies. The Kalman filter, and its many variations and extensions, is a key component of our work.