Source-linked AI summary
Structural Breaks in Time Series
Alessandro Casini, Pierre Perron
TL;DR
The chapter reviews methods for structural-change problems, including break detection, factor-regime analysis, and retrospective forecast stability. It compares testing procedures and reports that double-maximum tests are especially useful, with power nearly matching tests tailored to the correct number of breaks.
Problem
Structural-change analysis requires estimating break points and determining the number of factors, while forecast stability must be assessed retrospectively across in-sample and out-of-sample periods.
Method
The chapter surveys Wald-based, exponential, mean, double-maximum, sequential, unit-root-weighted, and related procedures for testing structural changes.
Results
Double-maximum tests are described as arguably the most useful for detecting structural changes, with power almost as high as tests using the correct number of breaks.
Takeaways & Limitations
For structural-change detection, double-maximum tests avoid requiring the number of breaks to be specified while retaining near-best power.
Takeaways & Limitations
The surveyed methods do not yet achieve the full generality available using standard procedures, although the approach remains promising for very large datasets.
Abstract
from arXiv · showhide
This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models. Substantial advances have been made to cover models at a level of generality that allow a host of interesting practical applications. These include models with general stationary regressors and errors that can exhibit temporal dependence and heteroskedasticity, models with trending variables and possible unit roots and cointegrated models, among others. Advances have been made pertaining to computational aspects of constructing estimates, their limit distributions, tests for structural changes, and methods to determine the number of changes present. A variety of topics are covered. The first part summarizes and updates developments described in an earlier review, Perron (2006), with the exposition following heavily that of Perron (2008). Additions are included for recent developments: testing for common breaks, models with endogenous regressors (emphasizing that simply using least-squares is preferable over instrumental variables methods), quantile regressions, methods based on Lasso, panel data models, testing for changes in forecast accuracy, factors models and methods of inference based on a continuous records asymptotic framework. Our focus is on the so-called off-line methods whereby one wants to retrospectively test for breaks in a given sample of data and form confidence intervals about the break dates. The aim is to provide the readers with an overview of methods that are of direct usefulness in practice as opposed to issues that are mostly of theoretical interest.
Abstract
This chapter reviews estimation, testing, computation, and inference for linear models with structural changes, spanning stationary, integrated, cointegrated, panel, factor, quantile, and endogenous-regressor settings. It emphasizes practically useful off-line methods for detecting breaks, estimating their dates, and determining their number.
- Modeling framework: The framework covers partial structural change models with stationary or integrated regressors, trends, cointegrated relationships, common breaks, and restrictions across regimes.Restricting coefficients to remain identical across regimes preserves consistency and break-date convergence rates, while valid restrictions can improve finite-sample precision and test power.
- Break-date inference: Break-date estimates have model-dependent inference: cointegrating regressions require jointly constructed confidence intervals, while some stationary-regressor cases yield asymptotically independent dates.Other parameter estimates can have the same distribution as if break dates were known, despite break-date estimates themselves having distinct convergence behavior.
- Computation and estimation: Computational advances reduce the burden of global minimization, replacing standard grid searches of order O(T m) with methods whose computation can be order O(T) for very large samples.The standard estimator is least squares, minimizing the overall sum of squared residuals; the review also emphasizes that instrumental variables are unnecessary in the discussed endogenous-regressor setting.
- Break-date inference: Confidence-set performance varies across methods: some procedures under-cover with small breaks, while others attain better coverage at the cost of longer sets, potentially spanning the whole sample.Continuous-record methods are reported to provide accurate convergence rates and relatively short confidence sets across break magnitudes and locations.
- Determining break numbers: Sequential estimates of the number of breaks can outperform information criteria, but the procedure should not be applied mechanically because it may stop too early.Estimating breaks one at a time can also produce different limit distributions from simultaneous estimation, and the sequential result fails for linear-trend breaks.
- Testing for breaks: For distant alternatives, Exp-type tests are optimal under equal weighting, whereas Mean-type tests are inferior to Sup- and Exp-type tests by approximate Bahadur efficiency.The cited results recommend Sup- or Exp-Wald tests and advise avoiding tests based on the LM statistic.
- Testing for breaks: Tests can have serious power and size problems when the number of breaks exceeds the number modeled, regressors or errors are strongly serially correlated, or variance shifts are unaccounted for.Finite-sample size distortions are especially concerning under strong serial correlation, and some procedures become unreliable with lagged dependent variables.