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Keywords = sup Wald test

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19 pages, 380 KiB  
Article
Bootstrap Confidence Intervals for Multiple Change Points Based on Two-Stage Procedures
by Li Hou, Baisuo Jin, Yuehua Wu and Fangwei Wang
Entropy 2025, 27(5), 537; https://doi.org/10.3390/e27050537 - 17 May 2025
Viewed by 481
Abstract
This paper investigates the construction of confidence intervals for multiple change points in linear regression models. First, we detect multiple change points by performing variable selection on blocks of the input sequence; second, we re-estimate their exact locations in a refinement step. Specifically, [...] Read more.
This paper investigates the construction of confidence intervals for multiple change points in linear regression models. First, we detect multiple change points by performing variable selection on blocks of the input sequence; second, we re-estimate their exact locations in a refinement step. Specifically, we exploit an orthogonal greedy algorithm to recover the number of change points consistently in the cutting stage, and employ the sup-Wald-type test statistic to determine the locations of multiple change points in the refinement stage. Based on a two-stage procedure, we propose bootstrapping the estimated centered error sequence, which can accommodate unknown magnitudes of changes and ensure the asymptotic validity of the proposed bootstrapping method. This enables us to construct confidence intervals using the empirical distribution of the resampled data. The proposed method is illustrated with simulations and real data examples. Full article
(This article belongs to the Special Issue Statistical Methods for Modeling High-Dimensional and Complex Data: Second Edition)
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39 pages, 560 KiB  
Article
Structural Break Tests Robust to Regression Misspecification
by Alaa Abi Morshed, Elena Andreou and Otilia Boldea
Econometrics 2018, 6(2), 27; https://doi.org/10.3390/econometrics6020027 - 22 May 2018
Cited by 1 | Viewed by 10068
Abstract
Structural break tests for regression models are sensitive to model misspecification. We show—analytically and through simulations—that the sup Wald test for breaks in the conditional mean and variance of a time series process exhibits severe size distortions when the conditional mean dynamics are [...] Read more.
Structural break tests for regression models are sensitive to model misspecification. We show—analytically and through simulations—that the sup Wald test for breaks in the conditional mean and variance of a time series process exhibits severe size distortions when the conditional mean dynamics are misspecified. We also show that the sup Wald test for breaks in the unconditional mean and variance does not have the same size distortions, yet benefits from similar power to its conditional counterpart in correctly specified models. Hence, we propose using it as an alternative and complementary test for breaks. We apply the unconditional and conditional mean and variance tests to three US series: unemployment, industrial production growth and interest rates. Both the unconditional and the conditional mean tests detect a break in the mean of interest rates. However, for the other two series, the unconditional mean test does not detect a break, while the conditional mean tests based on dynamic regression models occasionally detect a break, with the implied break-point estimator varying across different dynamic specifications. For all series, the unconditional variance does not detect a break while most tests for the conditional variance do detect a break which also varies across specifications. Full article
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