To remove seasonal nonstationarity of the series, the first seasonal differencing is applied:
wt = Et - Et-1 - Et-12 + Et-13; t= 14,15,… (1) Where wt is the first seasonal differencing of ground-water level Et. A spike at the first seasonal lag 12(|t-value|>1.6) appear on both acf and pacf (Figure 4), indicating that the period of differencing is 12 months.

(a)

(b)

Figure 3. The autocorrelation function (ACF)
(a) the raw monthly time series;
(b) the time series obtained through the first differencing

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(b)

Figure 4. The autocorrelation function (ACF) and the partial autocorrelation (PACF) for the time series obtained from the first seasonal differencing.

3.2 Estimation
The parameters for each model are estimated with the ARIMA module of MINITAB. The results are summarized in Table 3. The constant terms of all cases are negligibly small since the modeled differencing series has a nearly zero mean. The good quality of the coefficients are significantly greater than zero(|t-value|>2.0) and satisfy the stationarity conditions. Absolute values for all coefficients are also significantly different from 1.