Nonlinear time series modeling of some Canadian river flow data

In hydrology the ability to model the average daily river flow for rivers plays an important role in the prediction of possible disasters such as flooding. The analysis of data and the accuracy of predictions rely on fitting suitable models to such data. In this practicum we investigate nonlinear time series modeling and In particular we study the theory of two approaches to model such time series. One approach assumes the underlying random structure of the time series is bilinear. The second approach uses wavelet smoothing techniques to decompose the time series into a wavelet smoothed component and a random component. The random component is then modeled by a suitable linear or bilinear process. By investigating the structure of the autocorrelation and third order cumulants, we find that the pure bilinear process is best for the data sets under study. Models were fitted to six time series data sets based on the average daily river flow variable for six rivers in Canada using both approaches. A simulation study was conducted to establish the suitability of the models by comparing its performance to the original time series. The bilinear approach was not favorable in modeling average daily river flow. However, the wavelet methodology illustrated an attractive technique to model such a time series