One step ahead forecasting using

When dealing with time series the one step ahead forecasting problem based on experimental data is the problem of estimating the autoregression function of the underlying process When minimizing the expected forecast ing error is the main goal the exible approach has to be used to be able to adjust the complexity of the model to the complexity of the data Multilay ered perceptrons are a popular example of such a exible approach but not the only one Other methods such as kernel approximator e g Naradaya Watson regressor regression spline or wavelet regressor can also be used But whatever exible approach is the main issue remains the control of the complexity of the exible approximator Noise injection in the inputs is an e cient technique to do so The complexity of the regessor is then adjusted thanks to the quantity variance of injected noise This quantity is tuned using a bootstrap estimation of the forecasting error One unexpected e ect of this approach is the possibility to prove the consistency of the estimator under some assumptions about the underlying process who generates the time series The two main assumptions are the process is varying signi cantly and the process is bounded Furthermore the boundary conditions imply to eliminate the tendency for the remaining process to be bounded This theoret ical result permits to design a methodology for using multilayered perceptrons to forecast The whole approach was applied successfully to forecast the daily water consumption in the south of Paris