State analysis of nonlinear systems using local canonical variate analysis

Time series analysis is concerned with the evolution of univariate or multivariate time series and especially with the functional form underlying the evolution of the time series values. Key issues include the determination of state rank, Lyapunov exponents, attractor form, and prediction of future values. Numerous papers have proposed procedures for prediction of future time series values based on past response values. We propose and demonstrate a method for deriving an approximate state space model of a nonlinear system from time series data. The data may be multivariate, and may include both input and response values. The method, which we call local canonical variate analysis, estimates state rank, describes the state evolution, and predicts future response values. A detailed background of local canonical variate analysis is provided and the procedure is applied to several time series generated by nonlinear oscillatory systems