Structural break

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Linear regression with a structural break

In

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.[4]

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 K for K ∈ [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 forms of structural breaks

Other challenges occur where there are:

Case 1: a known number of breaks in mean with unknown break points;
Case 2: an unknown number of breaks in mean with unknown break points;
Case 3: breaks in variance.

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.[7][5][6] Bayesian methods exist to address these difficult cases via Markov chain Monte Carlo inference.[8][9]

In general, the

homoskedasticity across break points for finite samples;[4] 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 (IID) normal errors.[11] A method developed by Bai and Perron (2003) also allows for the detection of multiple structural breaks from data.[13]

The MZ test developed by Maasoumi, Zaman, and Ahmed (2010) allows for the simultaneous detection of one or more breaks in both mean and variance at a known break point.[4][14] The sup-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 an unknown break point.[4]

Structural breaks in cointegration models

For a cointegration 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.

Statistical packages

There are many

GAUSS, and Stata, 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]

See also

References

  1. S2CID 150379490
    . 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.
  2. ^ Kruiniger, Hugo (December 2008). "Not So Fixed Effects: Correlated Structural Breaks in Panel Data" (PDF). IZA Institute of Labor Economics. pp. 1–33. Retrieved 20 February 2019.
  3. doi:10.1257/jep.15.4.117
    .
  4. ^
    S2CID 126189844
    . The hypothesis of structural stability that the regression coefficients do not change over time is central to all applications of linear regression models.
  5. ^
    doi:10.1257/jep.15.4.117
    .
  6. ^
    ISBN 9780273753568
    . 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
  7. ISBN 978-0-07-066005-2
    .
  8. S2CID 61014871
    .
  9. ^ a b Li, Yang; Zhao, Kaiguang; Hu, Tongxi; Zhang, Xuesong. "BEAST: A Bayesian Ensemble Algorithm for Change-Point Detection and Time Series Decomposition". GitHub.
  10. S2CID 120051935
    .
  11. ^
    JSTOR 2951764. Archived
    (PDF) from the original on 6 November 2017.
  12. S2CID 55464774. Archived from the original
    (PDF) on 6 November 2017.
  13. hdl:10.1002/jae.659
    .
  14. doi:10.1016/j.econmod.2010.07.009
    .
  15. doi:10.1111/j.1468-0084.1996.mp58003008.x
    .
  16. S2CID 121999615
    .
  17. ISBN 978-0-387-77316-2
    .
  18. ^ Hyndman, Rob; Killick, Rebecca. "CRAN Task View: Time Series Analysis. Version 2023-09-26".
  19. ^ Achim, Zeileis; Leisch, Friedrich; Hornik, Kurt; Kleiber, Christian. "strucchange: Testing, monitoring, and dating structural changes".
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