How to find a change in the historical time-series data?
Long ago I have developed a method to do that which is based on EV data (Exception Value - a magnitude of anomalies collected historically). Idea: any change occurred first would appear as anomaly and then become a normality (norm), so collecting and analyzing a severity of all anomalies opens possibility to find phases in the history with different patterns. To detect that mathematically one needs just finds all roots of the following equation: EV(t)=0 , where t is time. But it is too simple as that might give you too many change points. To control the the sensitivity of detecting change points the method should have some sensitivity tuning parameters,such as following:
N - normality confidence band in percentiles = UCL-LCL (if it is 100%, that means all observations is normal, 0% means all observations abnormal)
Where UCL is upper control limit and LCL is lower control limit. Why "||" (absolute value)? To catch two types of changes: going up- and downwards.