Structural break

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A structural break is a sudden change over time in the relationships modeled by regression. If a model’s parameters shift and we don’t notice, forecasts can become very unreliable.

Chow test and simple cases
- For a single known break at time K, the Chow test checks if the regression coefficients are the same before and after K. It also assumes the error variance doesn’t change across the break.

When breaks are unknown or variance can change
- If the break point isn’t known or variance changes, the Chow test isn’t appropriate. Other tools are used:
- CUSUM and CUSUM-sq tests look at accumulated residuals to see if coefficients stay the same.
- Bounds test is another option to check for instability.
- sup-Wald, sup-LM, and sup-LR tests (Andrews) are designed for unknown numbers and locations of breaks. They are more powerful than CUSUM and are commonly used for detecting multiple breaks in the mean. They are usually asymptotic (valid as sample size grows) and assume constant variance across breaks; an exact version of sup-Wald exists for certain simple models.

Multiple breaks and other features
- Bai and Perron (2003) provide methods to detect multiple structural breaks.
- The MZ family (Maasoumi, Zaman, Ahmed, 2010) tests for breaks in both the mean and the variance if a break point is known; the sup-MZ version (2016) handles unknown break points.

Cointegration cases
- For cointegration models, Gregory–Hansen (1996) handles one unknown break; Hatemi–J (2006) allows two unknown breaks; Maki (2012) covers multiple breaks.

Practical notes and software
- Many statistical packages (R, GAUSS, Stata, and others) can test for structural breaks.
- Time series resources list various changepoint detection methods, including classical and Bayesian approaches.