Comparative study among different time series models applied to monthly rainfall forecasting in semi-arid climate condition

The aim of this study is to investigate the ability of different time series models in forecasting monthly rainfall. In order to do this, monthly rainfall data were collected from 9 rainfall stations in North Khorasan province (North east of Iran) from 1989 to 2012. R software was used to predict the highest rainfall in these 9 rain gage stations for the time period 2002–2012 using monthly highest rainfall data of 1989–2002. In this study, AR, MA, ARMA, ARIMA, and SARIMA with 11 different structures based on trial and error were examined. Because the trend, seasonal and jump components are deterministic components, it is not necessary to model these components, but modeling of random component is very important for rainfall forecasting. So, the main data series was decomposed (for AR, MA and ARMA models) and the random part has been modeled. After that, the random component was collected with the seasonal and trend component and the amount of rainfall was simulated. But for ARIMA and SARIMA, models fitted on original series. The result showed that in 33 % of data MA(2), in 22 % of data AR(1) and ARMA(2, 1) and in 11.11 % of data MA(1) and ARIMA(1, 1, 2) had the best performance in monthly rainfall forecasting. On the other hand, best time series model by change of data could vary. So, it is important to assess all the time series models for any area and any hydrological parameter.