| A new approach is proposed to model the relationship between two time series, perturbed by correlated noise. The functional form of this relationship (the transfer function) is unknown but assumed to be smooth. We propose to model the transfer function by nonparametric smoothing methods and model the noise as a stationary, invertible autoregressive-moving average process of finite orders. The estimation procedures are introduced and the asymptotic properties of the estimators are discussed. The finite-sample properties of the estimators are studied through simulation studies and real-life examples. The issues of nonstationary noise and multiple input variables are also addressed. By using nonparametric smoothing methods to model the transfer function, the model is very flexible and can be applied on highly nonlinear relationship of unknown form; by modelling the noise explicitly, the correlation is removed so the transfer function can be estimated more efficiently. Additionally, the estimated correlation structure can be used to improve the forecasting performance. |
