Forecasting by Stochastic Models to Inflow of Karkheh Dam at Iran

Forecasting the inflow of rivers to reservoirs of dams has high importance and complexity. Design and optimal operation of the dams is essential. Mathematical and analytical methods use for understanding estimating and prediction of inflow to reservoirs in the future. Various methods including stochastic models can be used as a management tool to predict future values of these systems. In this study stochastic models (ARIMA) are applied to records of mean annual flow Karkheh river entrance to Karkheh dam in the west of Iran. For this purpose we collected annual flow during the period from 1958/1959 to 2005/2006 in Jelogir Majin hydrometric station. The available data consists of 48 years of mean Annual discharge. Three types of ARIMA (p, d, q) models (0, 1, 1), (1, 1, 1) and (4, 1, 1) suggested, and the selected model is the one which give minimum Akaike Information Criterion (AIC). The Maximum Likelihood (ML), Conditional Least Square (CLS) and Unconditional Least Square (ULS) methods are used to estimate the model parameters. It is found that the model which corresponds to the minimum AIC is the (4, 1, 1) model in CLS estimation method. Port Manteau Lack of fit test and Residual Autocorrelation Function (RACF) test are applied as diagnostic checking. Forecasting of annual inflow for the period from 2006 to 2015 are compared with observed inflow for the same period and since agreement is very good adequacy of the selected model is confirmed

ANALYZING THE IMPACT OF HISTORICAL DATA LENGTH IN NON SEASONAL ARIMA MODELS FORECASTING

Different values of minimum data requirement for ARIMA models have been proposed. It also proposed to use as much data as they are available in formulating ARIMA models. This paper studied the impact of the size of the historical data on ARIMA models in forecasting accuracy. The study used 286 weekly records of amount of solid waste generated in Arusha City to formulate four ARIMA models using different data lengths or size. The first model, M1 used 30 observations, the second model, M2 used 60 observations, the third model M3 used 120 observations and the fourth model, M4 used 260 observations all of which are the most recent. A total of 26 observations were held out for validation. The precision in forecasting was tested using MAPE, RMSE and MAD.  The results indicated variation in precision. M3 performed best in one-week ahead and 9 – 12 weeks ahead while M4 did best in 2 – 8 weeks and also for 13 weeks  and above. M1 was the worst model in forecasting. Keywords: ARIMA models, MAPE, RMSE, MAD, Forecastin