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Discrimination of time series data can be carried out either in the frequency domain or in the time domain. Applications have been found useful in certain areas such as seismology and medicine. To date most discriminative work has been carried out for linear and stationary time series models. This paper extends the theory by considering the discrimination of state space models which can then also include linear models. A CUSUM approach is adopted to discriminate between two models, although standard CUSUM methods can not be used because of the lack of independence. The CUSUM method allows the discrimination to be viewed as a sequential method where a decision needs to be made as soon as reasonably possible.