Structural break


In econometrics and statistics, a structural break is an unexpected change over time in the parameters of regression models, which can lead to huge forecasting errors and unreliability of the model in general. This issue was popularised by David Hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and therefore we must routinely test for structural stability. Structural stability − i.e., the time-invariance of regression coefficients − is a central issue in all applications of linear regression models.

Structural break tests

A single break in mean with a known breakpoint

For linear regression models, the Chow test is often used to test for a single break in mean at a known time period for. This test assesses whether the coefficients in a regression model are the same for periods and.

Other forms of structural breaks

Other challenges occur where there are:
The Chow test is not applicable in these situations, since it only applies to models with a known breakpoint and where the error variance remains constant before and after the break.
In general, the CUSUM and CUSUM-sq tests can be used to test the constancy of the coefficients in a model. The bounds test can also be used. For cases 1 and 2, the sup-Wald, sup-LM, and sup-LR tests developed by Andrews may be used to test for parameter instability when the number and location of structural breaks are unknown. These tests were shown to be superior to the CUSUM test in terms of statistical power, and are the most commonly used tests for the detection of structural change involving an unknown number of breaks in mean with unknown break points. The sup-Wald, sup-LM, and sup-LR tests are asymptotic in general, and involve the assumption of homoskedasticity across break points for finite samples; however, an exact test with the sup-Wald statistic may be obtained for a linear regression model with a fixed number of regressors and independent and identically distributed normal errors. A method developed by Bai and Perron also allows for the detection of multiple structural breaks from data.
The MZ test developed by Maasoumi, Zaman, and Ahmed allows for the simultaneous detection of one or more breaks in both mean and variance at a known break point. The sup-MZ test developed by Ahmed, Haider, and Zaman is a generalization of the MZ test which allows for the detection of breaks in mean and variance at an unknown break point.

Structural breaks in cointegration models

For a cointegration model, the Gregory–Hansen test can be used for one unknown structural break, and the Hatemi–J test can be used for two unknown breaks.

Statistical packages

There are several statistical packages that can be used to find structural breaks, including R, GAUSS, and Stata, among others.