3.1 Identification
The first step is to plot the data for the monthly groundwater-level time series for 7 years (Figure 1). Data for the first 5 years are used for constructing the ARIMA model and the remaining years are reserved for evaluation. A simple linear regression model is used to characterize the trend component. The result of regression analysis is shown in Table 1. The trend of the overall groundwater-level develops through time. A clear seasonal pattern, with low levels from November to April and high levels from February to August, emerges from the data gathered.

Table 1. Results fromthe linear regression model
The first insight into the statistical properties of the time series is shown in Table 2. Performing the first differencing on the groundwater-level series reduces the series mean from -25.46 to 0.03. The first differencing often results in a stationary mean value of approximately zero (Figure 2).

Table 2. Various statistics of the raw data and of the first differencing

Data	Max (m)	Min (m)	Mean (m)	Variance
Raw	-16.95	-31.98	-25.46	11.852
First differencing	5.21	-7.60	0.03	5.478

Figure 1. Monthly groundwater-level data and regression model.

Figure 2. First differencing sequence plot.

Further illustration of the time series is obtained from the estimated autocorrelation function (ACF) and partial autocorrlation function (PACF). As shown in Figure 3, lags up to 37 months long are taken. The acf in Figure 3 dies down slowly in a damped sine-wave pattern, indicating that the raw data is nonstationary. Significant correlations(|t-value|>1.6) exist at the lag 1 and lag 2 phases in Figure 3(a). Spikes exist, indicating that the model can be mixed with the autoregressive and moving average models with each seasonal term.