Stochastic modeling of Mahi river inflows – A case study

Monthly inflow data of Mahi river for a period of 76 years (1928–2003) were collected. Fourier analysis was performed to obtain periodic component so that the stochastic series may be obtained by removing the periodic component from the monthly inflow series. Stochastic series was standardized and normalized to make the inflow series normally distributed. ACF, PACF, IACF and IPACF analyses were performed to identify the class and order of stochastic models. Twelve models of ARMA family, in which AR term ranged from 1 to 6 and MA term varied from 1 to 2, were identified for investigation. The first 74 years data were used for parameters estimation of the identified models. The parameters of six models, namely, ARMA(1,1), ARMA(2,1), ARMA(3,1), ARMA(1,2), ARMA(2,2), ARMA(4,2) were found to be significant. All the six models passed the validation tests. Regeneration of series was made by all the six models for the period of 1928 to 2001. Minimum mean square error (MMSE) criterion was used for selection of best model. It revealed that ARMA(3,1) model was proved to be most appropriate model. One-time step ahead monthly forecast were made by ARMA(3,1) for the period of 2002–2003. Values of correlation coefficient between observed and generated monthly inflow series for the period (2002–2003) was found to be 0.912 showing adequacy of developed model.