An Adaptive Structural Model When There is a Major Level Change

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In analyzing time series, estimating the level or the current mean of the process plays an important role in understanding its structure and in being able to make forecasts. The studies the class of time series models where the level of the process is assumed to follow a random walk and the deviation from the level follow an ARMA process. The estimation and forecasting problem in a Bayesian framework and uses the Kalman filter to obtain forecasts based on estimates of level. In the analysis of time series, we usually make the assumption that the time series is generated by one model. However, in many situations the time series undergoes a structural change at one point in time. For example there may be a change in the distribution of random variables or in parameter values. Another example occurs when the level of the process changes abruptly at one period. In order to study such problems, the assumption that level follows a random walk process is relaxed to include a major level change at a particular point in time. The major level change is detected by examining the likelihood raio under a null hypothesis of no change and an alternative hypothesis of a major level change. The author proposes a method for estimation the size of the level change by adding one state variable to the state space model of the original Kalman filter. Detailed theoretical and numerical results are obtained for th first order autoregressive process wirth level changes.