Monthly Rainfall Components in Ambon City: Evidence from the Serious Time Analysis

The purpose of this study is to prove whether rainfall in Ambon City contains seasonal components based on the characteristics of monthly rainfall history data in Ambon City. The data used is monthly rainfall data in Ambon City 2005.01-2017.12. The data is time series data from the BMKG Meteorology Station observation in Maluku Province. The time series analysis method used is ARIMA / SARIMA and Holt-Winter Exponential Smoothing. The results of this study have a good level of accuracy, namely using the results of analysis based on the values of information criteria, Ljung-Box Test, and RMSE. The results of the analysis prove that rainfall in Ambon City has a seasonal pattern.

Thus, this study was made different from previous studies. This study aims to prove whether rainfall in Ambon City contains seasonal components based on the characteristics of monthly rainfall history data in Ambon City. Because the data used is time series data, the analysis method applied is the time series method. The time series method used is ARIMA / SARIMA and Holt-Winter Exponential Smoothing. In addition, the data used is the latest data with a longer range than previous studies.

Data
The data used is the Ambon City monthly rainfall data for the period January

Method
This study uses a method that is able to detect seasonal patterns in rainfall. The analytical method used in this study is the ARIMA/SARIMA method and the Holt-Winter Exponential Smoothing method. Both of these methods have the ability to model non-seasonal data and seasonal data with good accuracy.
The analysis procedure carried out in this study is divided into two parts, namely modeling using the ARIMA/SARIMA method and modeling using the Holt-Winter Exponential Smoothing method. The analysis procedure using the ARIMA/SARIMA method is 1) Detecting seasonal patterns using a line plot; 2) Detect data stationary, patterns and seasonal periods using a plot of the Autocorrelation Function / Partial Autocorrelation Function (ACF / PACF); 3) Preparation of the ARIMA / SARIMA model; and 4) Identification of the best model based on information criteria values such as Akaike (1974) [1] Information Criteria = + 2 + + 1 ], Schwarzt Bayesian Information Criteria = + + + 1 and mean of square error [MSE]. In addition, serial correlation checks are performed using Ljung-Box (1978) [9] Where B is the backward shift operator, ∅ # , Φ / , ( ) , Θ 2 is the polynomial-polynomial with order , +, , in sequence, * ' is a random process and

. Results And Discussion
The rainfall data used is the result of observations for 13 years with the number of observations being 156 months. Statistically, the data is described in Table 1. Average rainfall indicates that rainfall in Ambon City is classified as moderate. Based on the Jarque-Bera test statistic, the data is not normally distributed at the 95% confidence level. Visually, the line plot of monthly rainfall data in Ambon City in the period 2005.01 -2017.12 is shown in Figure 1. The figure shows that rainfall data in Ambon City does not contain trends and is random. This indicates that rainfall data in Ambon City is stationary in the mean. The highest rainfall occurred in 2013, while the lowest rainfall occurred in 2005. Rainfall fluctuated every year with a high tendency of rainfall to occur from May to August, while in other months rainfall tends to be lower.  In addition to Figure 1, the ACF and PACF plots shown in Figure 2 can be used to identify trends and seasonality. The ACF plot for 36 lags does not slow down to 0, but forms a sinusoidal pattern. Whereas PACF plots do not form a certain pattern. This means that there is no trend, but indicates a seasonal effect in rainfall data in Ambon City. The results of the ACF plot observations show that 12, 24, 36 lags are positive and are above the limit. Thus, the seasonal period formed is 12 months.

ARIMA vs SARIMA
It is known that the ARIMA / SARIMA model is based on stationary data. The results of data stationarity analysis state that the results of the transformation of natural logarithms are data that is stationary (Figure 3). Thus, the data is good for modeling ARIMA and SARIMA.   Table 2 shows 20 ARIMA models and 20 best SARIMA models based on the information criteria values of AIC and SIC. Based on the table, the smallest AIC and SIC values are obtained by the seasonal models 3, 0, 1 1, 1, 1 6 and 2, 0, 0 1, 1, 1 6 . Based on these results, the SARIMA model is better than the non-seasonal ARIMA model.

Holt-Winter (HW)
The results of the analysis of rainfall data in Ambon City using the Holt (1957) [7]-Winter (1960) [15] Exponential Smoothing method are summarized in Table 4. The table shows three types of Holt-Winter models, namely non-seasonal models, seasonal multiplicative models, and seasonal additive models. The three models are based on optimal parameter values.  Table 4 shows the RMSE values of the three HW models. Based on the RMSE values, the HW seasonal multiplicative model is better than the other two HW models. This is because the RMSE value of the seasonal multiplicative model is smaller than the two models.

Conclusion
Statistically, it was found that the average rainfall in Ambon City was classified as moderate and the data was not normally distributed. Based on the results of the study using time series analysis, it is found that the model that best describes rainfall in Ambon City is a seasonal model. This is based on the results of comparative seasonal models with non-seasonal models, both in ARIMA / SARIMA and Holt-Winter Exponential Smoothing. Thus, it can be concluded that rainfall in Ambon City has a seasonal pattern.