The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes

In attempting to estimate the parameters of a linear regression system obeying two separate regimes, it is necessary first to estimate the position of the point in time at which the switch from one regime to the other occurred. The suggested maximum likelihood estimating procedure is based upon a direct examination of the likelihood function. An asymptotic and a small-sample test are suggested for testing the hypothesis that no switch occurred against the single alternative that one switch took place. The procedure is illustrated with a sampling experiment in which the true switching point is correctly estimated.