On change points in regression models

The report is devoted to description of a method of estimation of the parameters of a simple regression of an observed process Y
_t
on the predictive process X
_t
, t=1, 2,..., T, in situations where the observed response values depend not only on the predictor values and random factors, but also on the state of a hidden (unobservable) system with a finite set of states. The moments of transition between the states of the hidden system generate “change-points” in the process of observation, in which there is a change in the dependence of the response on the predictor. The regression model is constructed by the concatenation of the regression models for the segments of the partition generated by change-points. The report presents the results of testing the proposed method for the identification change-points for the problem of the substitution of a coin.