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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Elliott, G., Müller, U.K (2007) Confidence sets for the date of a single break in linear time series regressions | 1.000 | 10 | 4 | 100% |
| 2 | Yao, Y (1987) Approximating the distribution of the ML estimate of the change-point in a sequence of independent random variables | 1.000 | 6 | 4 | 100% |
| 3 | Casini, A., Perron, P (2021) Continuous record Laplace-based inference about the break date in structural change models self | 1.000 | 5 | 3 | 100% |
| 4 | Bai, J (1997) Estimation of a change-point in multiple regression models | 0.982 | 19 | 7 | 95% |
| 5 | Bai, J., Perron, P (1998) Estimating and testing linear models with multiple structural changes self | 0.950 | 7 | 3 | 86% |
| 6 | Chang, 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 self | 0.928 | 4 | 3 | 100% |
| 7 | Casini, A., Perron, P (2020) Generalized Laplace inference in multiple change-points models self | 0.811 | 4 | 2 | 100% |
| 8 | Nelson, D.B., Foster, D.P (1994) Asymptotic filtering theory for univariate ARCH models | 0.811 | 4 | 2 | 100% |
| 9 | Barndorff-Nielsen, O.E., Shephard, N (2004) Econometric analysis of realised covariation: high frequency based covariance, regression and correlation in financial economics | 0.737 | 4 | 3 | 50% |
| 10 | Casini, A., Perron, P (2020) Continuous record asymptotics for structural change models self | 0.737 | 3 | 3 | 67% |
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