Nonlinear Time Series Models: An Application on Amount of Water Flow of Blue Nile River Measured at Eldaim Station

Merdi Ahmed Orsud; Bassam Younis Ibrahim

Merdi Ahmed Orsud Faculty of Mathematical & Computer Sciences, University of Gezira, Medani, Sudan
Bassam Younis Ibrahim Sudan University of Science and Technology

Abstract

This paper had undertaken nonlinear time series modelling

and in particular, discussed wavelet smoothing technique to

decompose the time series into a wavelet smoothed component

and a random component. The random component was then

modelled by an appropriate linear ARIMA process or diagonal

pure bilinear process.

Before smoothing technique was applied, flow data was tested

for linearity and then filtered. By investigating the plot of the

third cumulant, it was found that diagonal pure bilinear process

of order two was the 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 with the actual time series data.

The wavelet smoothing technique demonstrated an

attractive technique to model such a time series data.

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