How to characterize abrupt change?

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?

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If the observations of your time series data are correlated with the immediately previous observations, the paper by Chen and Liu (1993)[1] may interest you. It describes a method to detect level shifts and temporary changes in the framework of autoregressive moving-average time series models.

[1]: 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

Source : Link , Question Author : user2230101 , Answer Author : Glen_b

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