FORECASTING A CHAOTIC TIME-SERIES USING AN IMPROVED METRIC FOR EMBEDDING SPACE

A method is presented for improving the accuracy of forecasts of future values of a time series of one variable of a chaotic dynamical system. The metric for the embedding space of time-delay vectors of time series values is obtained from a metric tensor whose components are varied to minimize root mean squared error of forecasts. The improvement of forecasts is demonstrated for time series of the Henon and Ikeda maps, the Lorenz system of coupled differential equations and the Mackey-Glass delay differential equation.