Synthetic Stream Flow Generation of River Gomti Using ARIMA Model

Abstract

Study of synthesizing of time series applies various stochastic models out of which autoregressive integrated moving average (ARIMA) model has proved to be an effective tool. Such models are useful to select the best fit model from the available past values of any time series. The objective of present study is to develop a methodology to synthetically generate the time series using ARIMA model for an Indian River Gomti at Gomti Barrage of Uttar Pradesh (U.P.), India. The approach for prediction of time series is based on the idea of predicting future values of an observed time series using a model with estimated regression parameters. ARIMA is a popularly adopted stochastic technique for the various studies in the water resources engineering where long futuristic data is necessary. The present model uses an iterative three-stage modelling approach. First stage is to identify and select model, which involves the checking of stationarity of the variables. Second stage comprises the checking of the seasonality of the dependent variables and to select the suitable model based on the plots of the autocorrelation and partial autocorrelation functions of the dependent time series data. Parameter estimation has been carried out using computation algorithms to arrive at coefficients which best fit the selected ARIMA (1, 1, 1) model. Model checking has been performed by testing whether the estimated model confirms to the least value of AIC and SBIC. By checking of the least value of the AIC and SBIC, the model is generated and hence the mathematical equation has been formulated for the generation of the forecasted stream flow for future time period from the original data of discharge collected from gauge site.