BaiPerron

Bai-Perron refers to a family of econometric methods for detecting multiple structural breaks in linear regression models when both the number and the locations of breaks are unknown. The methods were developed by Jushan Bai and Pierre Perron, with seminal work published in Econometrica in 1998 and subsequent refinements in 2003. The core idea is to estimate the regression separately within segments created by potential break dates, selecting breakpoints by minimizing the overall sum of squared residuals across all possible partitions.

The Bai-Perron approach provides procedures to test for the existence of breaks and to determine their number. It yields tests such as sequential sup-F statistics and related maximum statistics (e.g., UDmax, WDmax) for the null hypothesis of r breaks against r-1 breaks, along with criteria to choose the number of breaks (information criteria like BIC). Break dates are estimated by dynamic programming to render the search computationally feasible in large samples.

The model typically assumes a linear regression with possible breaks in intercepts and/or slopes, with mild regularity conditions on the error process. The method accommodates multiple breakpoints occurring at unknown dates, and can be applied to stationary or mildly dependent errors, with extensions for certain forms of heteroskedasticity.

Applications of Bai-Perron include macroeconomic time series, finance, and policy analysis, where regimes or structural shifts are believed to occur. Limitations include the need for sufficiently long samples, potential sensitivity to outliers or mis-specification of break structure, and reliance on asymptotic theory. Software implementations exist in various econometrics packages, reflecting its widespread use.