ABSTRACT

Nowadays, time series analysis is widely used in many branches of engineering, physical science, and economics, and it can be said that most branches of science lead to the study of data that are in the form of time series. A time series is a collection of statistical data collected regularly at certain time intervals. Time series analysis is a process through which the collected data is statistically analyzed. Time series analysis usually follows two purposes: first, understanding or modeling the random mechanism that leads to the observed series and second, forecasting future values of series takes place on the basis of its past.

Important characteristic of stochasticity of the hydrological phenomena has led the hydrologists to utilize the concepts of random variables and time series for modeling and forecasting hydrological variables. Application of time series in modeling of hydrological processes started four decades ago and reached its peak with Box and Jenkins models (ARMA- and ARIMA-type models). These models had been known as the linear time series models and not suitable for modeling nonlinear mechanisms. The ARCH and GARCH models are nonlinear time series models. Box and Jenkins models are used to combine different models to obtain new models with better performance. The ARIMA–GARCH models are a combinational model, which consist of two parts. The part of ARIMA models forecasts the mean of process and the part of GARCH models forecasts the variance of process in the time series.