Modeling ARIMA of air temperature of the southern Caspian Sea coasts

Abstract:The main purpose of time series analysis is to find a best fit to a data set that can be defined by a model that can be used for forecasting. In this paper, air temperature of the Caspian southern coasts was modeled by SARIMA or seasonal Autoregressive integrated moving average. A preliminary exploratory analysis of the monthly mean air temperatures of the Anzali, Ramsar and Babolsar synoptic stations was done to detect extreme values, homogeneity, step and monotonic trends. Then, each series was analyzed by a multiplicative decomposition method and the main components of the time series, namely trend (trt), and cyclical (clt), seasonal (snt) and irregular (random) changes (irt) were determined. Then model was performed and temperature was predicted. In preparation of the time series to be used in ARIMA model, the time series were transformed to normal and stationary series using Box-Cox and Differencing method. After selection of some suitable models and estimation of parameters by maximum likelihood method, independence and normality of model residuals ( ) should were considered to accuracy of data. Then Akaike information criteria (AIC) and (SBC) determined the best model: SARIMA (1,0,0)(0,1,1)12 for Anzali and Babolsar and SARIMA (0,0,2)(0,1,1)12 for Ramsar mean monthly temperature. Temperature at all stations was predicted with a high accuracy, in comparison with the actual data in two years 2005 and 2006 as the gauge by SARIMA model and multiplicative decomposition method. Correlation coefficient between the actual and fitted data was nearly 0.97 and the absolute and relative errors were very small.