Modelling and Prediction for Functional Relationships between Time-series

Much research in the sciences involves modelling and prediction of the functional relationship between simultaneous time series. In this paper we present a new method to infer functional relationship between simultaneous time series based on the modified version of Singular Value Decomposition method. We firstly extract the dominant relationships, perform pattern analyses on the dominant relationships, and construct the model equations of functional relationship between the time series through the time before the forecast period of interest. We then conduct predictions on the future values of one time series from another time series based on the model equations. Several regression schemes are proposed to serve as a prediction basis. The proposed model is applied to predict the real simultaneous health outcome time series. The simulation, the predictions and the real data show good agreement.