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Independent Errors

The only assumption of a change-point analysis is that of an independent error structure.  An independent error structure means that the data points X1, X2, X3, ...  are distributed as follows:

 Xi =  mi + ei

where the ei are independently distributed and mi represent the averages at each point in time.  It is further assumed that mi = mi-1 except for a small number of values of i called the change points.  This model is called the mean-shift model.  The purpose of the change-point analysis is to detect those values of i for which mi mi-1.

The assumption of independent errors is not nearly as restrictive as that of no serial correlation.  A change in the mean will cause serial correlation in the data but not violate the assumption of independent errors.  The test performed to verify the assumption of independent errors can distinguish between serial correlation created by shifts in the mean and serial correlation create by a dependent error structure.