Investigating the effect of observational data length on ARIMA modeling and forecasting accuracy: a case study of Kortian Stream watershed, Iran

Abstract

Using autoregressive integrated moving average (ARIMA) for modeling and predicting time series is worldwide, but how many available recorded observations can be used for modeling to achieve better results is debatable. The length of data can significantly affect the results of ARIMA models. This article investigates the effect of different lengths on prediction accuracy. For this purpose, 732 monthly data of streamflow of the Kortian gauging station at the Kortian Stream watershed were used. To study the impact of the type of data in terms of monthly or seasonal observation data on the accuracy of modeling results, monthly data were converted into seasonal data and the results of monthly and seasonal modeling were compared. Therefore, multiplicative ARIMA models were performed for the monthly and seasonal modeling. Compared with the seasonal modeling, the monthly modeling presented more precise results than the sum of the square errors of monthly and seasonal modeling, which were 0.9408 and 2.5, respectively. For the monthly modeling, five different lengths of data were used. The C1 model used the last 60 data, C2 used the last 120 recorded observations, C3 used the last 240 data, C4 used the last 480 observations, and C5 used the last 708 data. To test the precision of models, 24 observations were put aside. Among the C1 to C5 models, the C4 model presented the best results in predicting 2 years ahead and C1 had the worst results.