Theory and Application of an Estimation Model for Time Series with Nonstationary Means

Time series models of a complex nature, such as consumer brand switching analyses, have required assumptions of parameter stability because statistical models were not available to deal with parameter change. A model is developed here to estimate a stepwise change in the mean process of a Gaussian time series. Estimators which are small-sample efficient in a special sense are presented, along with examples and suggested applications of the method to brand switching problems.