4. Time Series Modeling

Modeling of time series involves dealing with the important temporal dimension, which represents and processes sequential inputs. Many statistical-based methods are used to model and forecast time series data such as autoregressive (AR) and autoregressive moving average (ARMA) models, autoregressive integrated moving average (ARIMA) model, and autoregressive moving average with exogenous (ARMAX) data. Time series modeling involves techniques that relate time series data as dependent variables to the predictors, which all are a function of time. Many examples of time series data exist in the field of water resources and environmental engineering, including streamflow data, rainfall data, and time series of total dissolved solids in a river. This variety makes the application of time series very interesting in those fields. Two major applications are usually followed up by the time series modeling: forecasting and synthetic data generation. This chapter reviews the basic mathematical representation as well as the applicable fields of the well-known time series models. In addition to the time series analysis, different models and applications are presented by different programs developed in MATLAB.