# Time Series ARIMA Model for Prediction of Daily and Monthly Average Global Solar Radiation: The Case Study of Seoul, South Korea

^{1}

Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea

^{2}

Department of Civil Engineering, Philadelphia University, P.O. Box 19392 Amman, Jordan

^{*}

Author to whom correspondence should be addressed.

Received: 15 January 2019 / Revised: 5 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019

Forecasting solar radiation has recently become the focus of numerous researchers due to the growing interest in green energy. This study aims to develop a seasonal auto-regressive integrated moving average (SARIMA) model to predict the daily and monthly solar radiation in Seoul, South Korea based on the hourly solar radiation data obtained from the Korean Meteorological Administration over 37 years (1981–2017). The goodness of fit of the model was tested against standardized residuals, the autocorrelation function, and the partial autocorrelation function for residuals. Then, model performance was compared with Monte Carlo simulations by using root mean square errors and coefficient of determination (R

^{2}) for evaluation. In addition, forecasting was conducted by using the best models with historical data on average monthly and daily solar radiation. The contributions of this study can be summarized as follows: (i) a time series SARIMA model is implemented to forecast the daily and monthly solar radiation of Seoul, South Korea in consideration of the accuracy, suitability, adequacy, and timeliness of the collected data; (ii) the reliability, accuracy, suitability, and performance of the model are investigated relative to those of established tests, standardized residual, autocorrelation function (ACF), and partial autocorrelation function (PACF), and the results are compared with those forecasted by the Monte Carlo method; and (iii) the trend of monthly solar radiation in Seoul for the coming years is analyzed and compared on the basis of the solar radiation data obtained from KMS over 37 years. The results indicate that (1,1,2) the ARIMA model can be used to represent daily solar radiation, while the seasonal ARIMA (4,1,1) of 12 lags for both auto-regressive and moving average parts can be used to represent monthly solar radiation. According to the findings, the expected average monthly solar radiation ranges from 176 to 377 Wh/m^{2}.*Keywords:*Forecasting; Time series modelling; ARIMA; SARIMA; Solar energy; Green energy; Photovoltaic systems; South Korea; Seoul