NONLINEAR TIME SERIES MODELLING: ORDER IDENTIFICATION AND WAVELET FILTERING Abbreviated title: Nonlinear time series modelling

In this paper we discuss an approach for modelling nonlinear time series data based on wavelet smoothing. The technique involves decomposing the series into two components a deterministic component which when extracted by wavelet ̄ltering leaves a random component which can be easily modelled using well known linear time series modelling techniques or by a simple diagonal pure bilinear model discussed in this paper. The two components are then combined to describe the series. We also discuss how patterns present in the third order cumulants of the diagonal pure bilinear time series model can be used to identify the order of the model. Simulated data and real time series examples are used to illustrate the techniques.