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Continuous Record Asymptotics for Change-Points Models

Alessandro Casini, Pierre Perron

arXiv 28 Mar 2018 · Mathematics — Statistics Theory · publishedJournal of Time Series Analysis (2025) · 8 citations (OpenAlex)

arXiv:1803.10881 · PDF · DOI · OpenAlex · Extracted main text

Abstract

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.

Citation extraction

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Elliott, G., Müller, U.K (2007) Confidence sets for the date of a single break in linear time series regressions1.000104100%
2Yao, Y (1987) Approximating the distribution of the ML estimate of the change-point in a sequence of independent random variables1.00064100%
3Casini, A., Perron, P (2021) Continuous record Laplace-based inference about the break date in structural change models self1.00053100%
4Bai, J (1997) Estimation of a change-point in multiple regression models0.98219795%
5Bai, J., Perron, P (1998) Estimating and testing linear models with multiple structural changes self0.9507386%
6Chang, S.Y., Perron, P (2018) A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models self0.92843100%
7Casini, A., Perron, P (2020) Generalized Laplace inference in multiple change-points models self0.81142100%
8Nelson, D.B., Foster, D.P (1994) Asymptotic filtering theory for univariate ARCH models0.81142100%
9Barndorff-Nielsen, O.E., Shephard, N (2004) Econometric analysis of realised covariation: high frequency based covariance, regression and correlation in financial economics0.7374350%
10Casini, A., Perron, P (2020) Continuous record asymptotics for structural change models self0.7373367%

Showing the top 10 of 64 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference0.51121
2Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models0.51121
3A Generalized Argmax Theorem with Applications0.51121
4Change-Point Analysis of Time Series with Evolutionary Spectra0.40511