The ARIMA method, time series analysis technique, was proposed to perform short-term ionospheric Total Electron Content (TEC) forecast and to detect TEC anomalies. The success of the method was tested in two major earthquakes that occurred in India (M 7.7 Bhuj EQ, on Jan 26, 2001) and Turkey (M 7.1 Van EQ, on Oct 23, 2011). For ARIMA analysis, we have taken 18 and 29 days of TEC data with a 2-h temporal resolution and train the model with an accuracy of 5.1 and 2.7-2.9 TECU for India and Turkey EQs, respectively. After training the model and optimizing hyper model parameters, we applied on 8 and 9 days' time-window to observe anomalies. In Bhuj EQ, the negative anomalies are recorded on Jan 19 and 22, 2001. Similarly, positive anomalies are recorded on Jan 23, 24, and 25, 2001. In Van EQ, we recorded a strong positive anomaly on Oct 21, 2011, and in the consecutive days before the earthquake, some weak negative anomalies have also observed. The results showed that ARIMA has an adequate short-term performance of the ionospheric TEC prediction and anomaly detection of the TEC time series.