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Detecting early or late changes in linear models with heteroscedastic errors
Author(s) -
Horváth Lajos,
Miller Curtis,
Rice Gregory
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12507
Subject(s) - heteroscedasticity , homoscedasticity , econometrics , mathematics , linear model , linear regression , consistency (knowledge bases) , statistics , null hypothesis , geometry
We construct and study a test to detect possible change points in the regression parameters of a linear model when the model errors and covariates may exhibit heteroscedasticity. Being based on a new trimming scheme for the CUSUM process introduced in Horváth et al. (2020), this test is particularly well suited to detect changes that might occur near the endpoints of the sample. A complete asymptotic theory for the test is developed under the null hypothesis of no change in the regression parameter, and consistency of the test is also established in the presence of a parameter change. Monte Carlo simulations show that our test is comparable to existing methods when the errors are homoscedastic. In contrast, existing methods developed for homoscedastic data are demonstrated to be ill‐sized and poorly performing in the presence of heteroscedasticity, while the proposed test continues to perform well in heteroscedastic environments. These results are further demonstrated in a study of the linear connection between the price of crude oil and the U.S. dollar, and in detecting changes points in asset pricing models surrounding the COVID‐19 pandemic.