A Time Series Analysis for the Monthly Variation of $SO_2$ in the Certain Areas

ARIMA model에 의한 서울시 일부지역 $SO_2$ 오염도의 월변화에 대한 시계열분석

The typical ARIMA model which was developed by Box and Jenkins, was applied to the monthly $SO_2$ data collected at Seoungsoo and Oryudong in metropolitan area over five years, 1982 to 1986. To find out the changing pattern of $SO_2$ concentration, autocorrelation and partial autocorrelation analysis were undertaken. The three steps of time series model building were followed and the residual series was found to be a random white noise. The results of this study is summarized as follows. 1) The monthly $SO_2$ series was found to be a non-stationary series which which has a periodicity of 12 months. After eliminating the periodicity by differencing, the monthly $SO_2$ series became a stationary series. 2) The ARIMA seasonal model of the $SO_2$ was determined to be ARIMA $(1, 0, 0)(0, 1, 0,)_{12}$ model. 3) The model equations based on the prediction were: for Seoungsoodong: $Y_t = 0.5214Y_{t-1} + Y_{t-12} - 0.5214Y_{t-13} + a_t$ for Oryudong: $Y_t = 0.8549Y_{t-1} + Y_{t-12} - 0.8549Y_{t-13} + a_t$ 4) The validity of the model identified was checked by compairing the measured $SO_2$ values and one-month-ahead predicted values. The result of correlation and regression analysis is as follows. Seoungsoodong: $Y = 0.8710X + 0.0062 r = 0.8768$ Oryudong : $Y = 0.8758X + 0.0073 r = 0.9512$