Robust estimation of multi-input transfer function model with structural change

A nonparametric regression model to estimate multi-input transfer function model is proposed. Issues and limitations of the parametric transfer function such as linearity, correlated inputs, misspecification errors, short time series and presence of structural change are addressed by the nonparametric model. Three modelling approaches were compared - parametric transfer function(ARMAX), nonparametric regression generalized additive model (GAM), and forward search and nonparametric bootstrap (FSNB) method. Simulation results show that GAM performs best under short time series. Moreover, GAM is robust under the presence of misspecification error and structural change, on the number of inputs, correlated inputs, and length of time series. ARMAX on the other hand performed better on longer time series and exponentially decaying form. Forward search and nonparametric bootstrap method performed the least among the three approach but the mean absolute percent error (MAPE) is stable under different conditions of structural change such as location and length of structural change. Overall, the nonparametric approach is superior and most efficient in fitting different form of transfer function especially when there is misspecification error and correlated inputs.