A Diagnostic Measure for Level Shifts in Time Series

A diagnostic measure used in regression analysis is considered for detection of level shifts in autoregressive time series. A detection measure based on extra-sum-of-squares principle for level shifts is developed. The asymptotic distribution of the detection measure is obtained. An iterative procedure for modeling time series in the presence of level shifts is proposed and an approximation of the effect of level shifts is suggested to perform the iterative procedure. An example is presented to illustrate the methodology.