Change points and switching regressions
The change point problem, and more specifically that of switching regressions, is often encountered in the field of applied statistics. Applications range from experiments in extra-sensory perception and continuous production processes to the rejection of kidney transplants and the success-rate of racing tipsters. Econometrics is another area in which switching regression models are often pertinent. The thesis comprises two parts: in Part One, previous work on the general change point problem is reviewed from a variety of different viewpoints, whilst in Part Two, we describe a new approach to the problem of switching regressions, when the transition is abrupt. Based on a simple statistic, Rt2, this approach is found to have a number of advantages over that using Quandt's statistic, lambda t. Though we demonstrate, by simulation, that the distribution of - log lambda t, has an approximately Pearson type III (Gamma) form, there appears to be no simple way of estimating the parameters of this distribution. However, the distribution of Rt2 for given t is known exactly and can be expressed in terms of hypergeometric functions. Associated exact tests of significance are thus derived, and simpler approximations are investigated. Approximations to an unconditional test, based on the maximum value of Rt2, are also given. The power of these tests are studied by simulation and compared with other approaches. It is suggested that the plot of Rt2 against t is a useful diagnostic aid in regression analysis. Its interpretation is very similar to the square of a multiple correlation coefficient. The shape of the plot can indicate changes in regression coefficients and indicate certain types of clustering in the variables. It can be used for regressions involving any number of regressor variables. Several case studies are given. Finally the use of this technique in identifying unknown change points (slippage) is investigated, and compared with standard techniques such as cusum.