Modeling and prediction of time-series data by orthogonal search and canonical variate analysis

The authors investigate two general methods of modeling and prediction, the orthogonal search method and canonical variate analysis approach, to time-series data. Nonlinear autoregressive moving average (ARMA) and state affine models are adopted for approximation and developed as one step predictors. An unknown nonlinear time-invariant system is assumed to have the Markov property of finite order so that the one step predictors are finite dimensional. No special assumptions are made about the model terms, model order or state dimensions. Computer simulations are presented for Lorenz attractor