A Statistical Framework for Detecting Structural Breaks in Linear Regression Models

In recent years, inference problems associated with linear models with structural changes are increasingly met within the statistical analysis of many real life problems. In the study of the relationship between yield data and explanatory variables in growth models, dependence studies in chemical reactions etc., it is very often noted that the relationship is of one type for a certain configuration of the values of the explanatory variables and of another type for a different configuration of the values of the explanatory variables. Such changes in the relationship are, sometimes sudden and sometimes gradual. In such circumstances, it is not possible to use the conventional theory of linear models which explicitly assumes a fixed rigid relationship throughout. Switching linear models are quite useful and provide better models for the data in such situations. Consider a manufacturing industry producing a particular consumer product. The profit margin of the company may follow a particular pattern (per capita) until a period when a new technology is introduced or the workers are given specialized training in handling the machines. From that period onwards the profit margin (per capita) may show a new pattern. This is an example of a sudden structural change.