With Application on Amount of Water Flow of Blue River Nile Measured at Eldaim Station

Abstract

This research undertakes nonlinear time series modelling and in particular discusses wavelet smoothing technique to decompose the time series into a wavelet smoothed component and a random component. The random component is then modelled by an appropriate linear ARIMA process or diagonal pure bilinear process. The research reviews the linear and some nonlinear time series models for univariate time series and gives some definitions and concepts in wavelet. Before smoothing technique was applied, flow data was tested for linearity and then filtered. By investigating the plot of the third cumulant find that diagonal pure bilinear process of order two is best for the data sets under study. diagonal Pure bilinear of order two model was fitted to time series data set based on the mean daily Blue Nile river flow variable at Eldaim Station, (during the period January 2005 to December 2006) using wavelet smoothing technique. A simulation technique was performed to find the appropriateness of the model by comparing its performance to the actual time series. The wavelet smoothing technique demonstrated an attractive technique to model such a time series.