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.