Determination of The Best Box-Jenkins’ Seasonal Model to Inflows of Reservoir of Bekhme Dam

Abstract

Prediction of water inflow to a reservoir is of great interest in the policy of the reservoir operation throughout the year. When significant amounts of inflow series entering to the reservoir are nondeterministic events, the utilization of stochastic models to check the reliability of the recorded data and forecast the future events become preferable. One of the most powerful and widely used methodology for forecasting time series is the class of models called the Box-Jenkins models. In this study, time series analysis was applied to records of 69 monthly mean inflows to Bekhme reservoir, in the northern part of Iraq, for the water year period from 1933 to 2006. Nine multiplicative seasonal models were fitted to this series; these were the seasonal autoregressive integrated (SARI) (1, 1, 0) × (1, 1, 0)12, (2, 1, 0) × (1, 1, 0)12, and (1, 1, 0) × (2, 1, 0)12 models, the seasonal autoregressive integrated moving average (SARIMA) (1, 1, 1) × (1, 1, 1)12, (2, 1, 2) × (1, 1, 1)12, and (1, 1, 1) × (2, 1, 2)12 models, and the seasonal integrated moving average (SIMA) (0, 1, 1) × (0, 1, 1)12, (0, 1, 2) × (0, 1, 1)12, and (0, 1, 1) × (0, 1, 2)12 models. The unconditional sum of squares method was used to estimate the parameters of the models and to compute the sum of squared errors for each one. It was found that the best model which corresponded to the minimum sum of squared errors was the SIMA (0, 1, 1) × (0, 1, 1)12 model. The estimated moving average parameters of this model were 0.378 and 0.953 for both θ and Θ respectively. The adequacy of this model was checked by plotting the normalized cumulative periodogram which does not indicate nonrandomness of the residuals. Forecasts of monthly inflow for the period from October, 2002, to September, 2006 were graphically compared with observed inflow for the same period and since agreement was very precise, adequacy of the selected model was confirmed.