Nonlinear Time Series Modeling Using Spline-based Nonparametric Models

In this paper we use the polynomial splines-based nonparametric transfer function method to study how river flow is affected by multiple factors. The highly nonlinear relationship between river flow and the independent variables (the transfer function) is modeled using polynomial spline, and the noise term assumed to follow a parametric Autoregressive (AR) model. The transfer function is modeled jointly with the AR parameters. Because of its flexibility, spline functions are ideal for modeling highly nonlinear relationships with unknown functional forms; by modeling the noise explicitly, the correlation in the data is removed so the transfer function can be estimated more effeciently. Additionally, the estimated AR parameters can be used to improve the forecasting performance. The proposed polynomial splines-based estimator is also highly computationally effecient. A comparison of the results show that the performance of this model is better than some widely accepted benchmark models.