Ineconometrics andstatistics, astructural break is an unexpected change over time in theparameters ofregression models, which can lead to hugeforecasting errors and unreliability of the model in general.[1][2][3] This issue was popularised byDavid 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 oflinear regression models.[4]
Forlinear regression models, theChow test is often used to test for a single break in mean at a known time periodK forK ∈ [1,T].[5][6] This test assesses whether the coefficients in a regression model are the same for periods[1,2, ...,K] and[K + 1, ...,T].[6]
Other challenges occur where there are:
TheChow 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.[7][5][6] Bayesian methods exist to address these difficult cases viaMarkov chain Monte Carlo inference.[8][9]
In general, theCUSUM (cumulative sum) and CUSUM-sq (CUSUM squared) tests can be used to test the constancy of the coefficients in a model. The bounds test can also be used.[6][10] For cases 1 and 2, thesup-Wald (i.e., thesupremum of a set ofWald statistics),sup-LM (i.e., the supremum of a set ofLagrange multiplier statistics), andsup-LR (i.e., the supremum of a set oflikelihood ratio statistics) tests developed byAndrews (1993, 2003) may be used to test for parameter instability when the number and location of structural breaks are unknown.[11][12] These tests were shown to be superior to the CUSUM test in terms ofstatistical power,[11] 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.[4] The sup-Wald, sup-LM, and sup-LR tests areasymptotic in general (i.e., the asymptoticcritical values for these tests are applicable for sample sizen asn → ∞),[11] and involve the assumption ofhomoskedasticity across break points for finite samples;[4] however, anexact test with the sup-Wald statistic may be obtained for a linear regression model with a fixed number of regressors andindependent and identically distributed (IID)normal errors.[11] A method developed by Bai and Perron (2003) also allows for the detection of multiple structural breaks from data.[13]
TheMZ test developed by Maasoumi, Zaman, and Ahmed (2010) allows for the simultaneous detection of one or more breaks in both mean and variance at aknown break point.[4][14] Thesup-MZ test developed by Ahmed, Haider, and Zaman (2016) is a generalization of the MZ test which allows for the detection of breaks in mean and variance at anunknown break point.[4]
For acointegration model, the Gregory–Hansen test (1996) can be used for one unknown structural break,[15] the Hatemi–J test (2006) can be used for two unknown breaks[16] and the Maki (2012) test allows for multiple structural breaks.
There are manystatistical packages that can be used to find structural breaks, includingR,[17]GAUSS, andStata, among others. For example, a list of R packages for time series data is summarized at the changepoint detection section of the Time Series Analysis Task View,[18] including both classical and Bayesian methods.[19][9]
Structural changes and model stability in panel data are of general concern in empirical economics and finance research. Model parameters are assumed to be stable over time if there is no reason to believe otherwise. It is well-known that various economic and political events can cause structural breaks in financial data. ... In both the statistics and econometrics literature we can find very many of papers related to the detection of changes and structural breaks.
The hypothesis of structural stability that the regression coefficients do not change over time is central to all applications of linear regression models.
An important assumption made in using the Chow test is that the disturbance variance is the same in both (or all) regressions. ...
6.4.4 TESTS OF STRUCTURAL BREAK WITH UNEQUAL VARIANCES ...
In a small or moderately sized sample, the Wald test has the unfortunate property that the probability of a type I error is persistently larger than the critical level we use to carry it out. (That is, we shall too frequently reject the null hypothesis that the parameters are the same in the subsamples.) We should be using a larger critical value. Ohtani and Kobayashi (1986) have devised a "bounds" test that gives a partial remedy for the problem.15
