Detection of Interventions at Unknown Times

Abstract

While the detection of changes in parameters when the time of change is a relatively standard statistical problem; the detection of changes when the time of change is unknown is a non-standard problem that is currently receiving considerable attention. A method of detecting change of regression parameters at unknown times has been presented in this chapter. A derivation of a likelihood ratio type statistic for detecting changes in regression parameters at unknown times is presented and distributional properties of the statistic are discussed in the chapter. The statistic is then applied to several periodic series. Models are then considered for improving the short and intermediate-term forecasting capacity of periodic models, yet, preserving both long-term predictive capacity and the clear meaning of the model parameters. The models are constructed so as to have certain properties of the autoregressive schemes, but to retain the basic properties of periodicity. The effect of present observations on the amplitude disappears in the long term; hence, the basic cycle defines the long-term prediction. An adaptive harmonic regression model of a doubly stochastic nature fitted to data indicates that such models are capable of improving both fits to the data and forecasts of future observations.