This question may be too basic. For a temporal trend of a data, I would like to find out the point where “abrupt” change happens. For example, in the first figure shown below, I would like to find out the change point using some statistic method. And I would like to apply such method in some other data of which the change point is not obvious (like the 2nd figure).So is there a common method for such purpose?
If the observations of your time series data are correlated with the immediately previous observations, the paper by Chen and Liu (1993) may interest you. It describes a method to detect level shifts and temporary changes in the framework of autoregressive moving-average time series models.
: Chen, C. and Liu, L-M. (1993),
“Joint Estimation of Model Parameters and Outlier Effects in Time Series,”
Journal of the American Statistical Association, 88:421, 284-297