Inference on locally ordered breaks in multiple regressions

Abstract

We consider issues related to inference about locally ordered breaks in a system of equations, as originally proposed by Qu and Perron (2007). These apply when break dates in di¤erent equations within the system are not separated by a positive fraction of the sample size. This allows constructing joint con…dence intervals of all such locally ordered break dates. We extend the results of Qu and Perron (2007) in several directions. First, we allow the covariates to be any mix of trends and stationary or integrated regressors. Second, we allow for breaks in the variance-covariance matrix of the errors. Third, we allow for multiple locally ordered breaks, each occurring in a di¤erent equation within a subset of equations in the system. Via some simulation experiments, we show …rst that the limit distributions derived provide good approximations to the …nite sample distributions. Second, we show that forming con…dence intervals in such a joint fashion allows more precision (tighter intervals) compared to the standard approach of forming con…dence intervals using the method of Bai and Perron (1998) applied to a single equation. Simulations also indicate that using the locally ordered break con…dence intervals yields better coverage rates than using the framework for globally distinct breaks when the break dates are separated by roughly 10% of the total sample size.

Efficiently Detecting Multiple Structural Breaks in Systems of Linear Regression Equations with Integrated and Stationary Regressors

“…More specifically, we focus on systems of equations with a mix of integrated and stationary regressors. Thus far, the literature on structural breaks has provided only few methods applicable to linear regressions with multiple equations and integrated regressors (see, for example, Bai et al, 1998;Li and Perron, 2017;Oka and Perron, 2018). Without prior knowledge about the structural breaks, methods are needed that precisely determine the number of structural breaks, their timing, and simultaneously estimate the model's coefficients.…”

“…Although estimators based on the penalized regression principle have become popular in the context of change-point problems, few prior studies apply them to linear regressions with integrated regressors (Schmidt and Schweikert, 2021;Schweikert, 2021) or linear regressions with multivariate responses (Gao et al, 2019;Safikhani and Shojaie, 2020). While existing approaches follow a specific-to-general principle utilizing a likelihood-based approach to sequentially increase the number of breakpoints in a model (Bai et al, 1998;Qu and Perron, 2007;Li and Perron, 2017;Oka and Perron, 2018), we take a general-to-specific approach shrinking down the number of breakpoint candidates to find the best fitting model. While the likelihood-based approach employs dynamic programming techniques and is computationally efficient in rather short samples with (possibly) many structural breaks, the proposed model selection approach is particularly useful for long samples with a moderate number of structural breaks (having computational costs linear in the number of observations).…”

“…A sequential break test can be used to determine the number of structural breaks. In related studies, Eo and Morley (2015), Li and Perron (2017), and Oka and Perron (2018) extend the likelihood-based approach in several directions. Eo and Morley (2015) propose confidence sets for the timing of structural break estimation in multiple equation regression models.…”

“…Our framework is flexible enough to allow for a mix of integrated and stationary regressors, as well as deterministic terms. Using simulation experiments, we show that the proposed two-step estimator performs competitively against the likelihood-based approach (Qu and Perron, 2007;Li and Perron, 2017;Oka and Perron, 2018) when trying to detect common breaks in finite samples. However, the two-step estimator is computationally much more efficient.…”

Structural Breaks in Time Series

“…Unlike the case with asymptotically distinct breaks, the distributions of the estimates of the break dates need to be considered jointly. Their analysis has been considerably extended to cover models with trends and integrated regresssors in Li and Perron (2017).…”