A note on monitoring time-varying parameters in an autoregression

We develop a sequential testing approach for a structural change in the parameters of an autoregression, which amounts to an adaptation of the monitoring procedure, outlined in Chu, Stichcombe and White (1996). This procedure has a controlled asymptotic size as one repeats the test. Our method can be used as a general misspecification test. We apply our method to monthly US industrial production in order to investigate if its autoregressive behavior and/or its innovation variance have changed during the twentieth century.