Chapter 3 - Introduction of multiple/multivariate linear and nonlinear time series models in forecasting streamflow process

Abstract

This chapter aims to introduce several multiple/multivariate linear and nonlinear time series models for forecasting streamflow process, which have widely been used in econometrics earlier. However, a few studies regarding the application of these models have been carried out in modern hydrology in recent years. For this purpose, to model conditional mean behavior of multiple streamflow time series as well as multivariate rainfall-runoff process, vector autoregressive without/with exogenous variables approach as the “multiple/multivariate linear” time series models were introduced. In addition, to capture conditional time-varying variance that may exist in the hydrologic time series, the bivariate diagonal vectorization heteroscedasticity model was applied. This model is one of the main multiple/multivariate generalized autoregressive conditional heteroscedasticity “nonlinear” time series models. In this regard, two recent studies of Iran were described in this chapter by applying the aforementioned time series models in forecasting streamflows in more detail.