This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, multidimensional time series scenarios. We use large sample simulation data for a range of values of sample sizes, lags, and number of time series to obtain an empirical estimation of the correct rejection regions for the particular combination of values of these variables. Furthermore, we use a regression modeling with interactions and covariate power combinations to parametrically extend these precise rejection regions to all combination of values of sample sizes, lags, and number of time series. Our results show that we attain almost perfect Type I error rates across all scenarios. These findings will improve the goodness-of-fit diagnostics for multivariate time series analysis.
","abstract_html":"<p>This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, multidimensional time series scenarios. We use large sample simulation data for a range of values of sample sizes, lags, and number of time series to obtain an empirical estimation of the correct rejection regions for the particular combination of values of these variables. Furthermore, we use a regression modeling with interactions and covariate power combinations to parametrically extend these precise rejection regions to all combination of values of sample sizes, lags, and number of time series. Our results show that we attain almost perfect Type I error rates across all scenarios. These findings will improve the goodness-of-fit diagnostics for multivariate time series analysis.</p>","abstract_has_math":false,"creators":["Huang, Minhao"],"institution":null,"degree_name":null,"degree_level":"Thesis","degree_discipline":"Computational and Data Sciences","degree_department":null,"school":null,"contributors":["Cyril Rakovski","Adrian Vajiac","Sidy Danioko"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05-01T07:00:00Z","date_published":"2024-05-01T07:00:00Z","updated_at":"2026-07-24T01:38:37Z","subjects":["goodness-of-fit","Ljung-Box","multivariate","time series","Applied Statistics","Data Science","Longitudinal Data Analysis and Time Series","Multivariate Analysis","Statistical Methodology","Statistical Models"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.chapman.edu/cads_dissertations/44","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cyril Rakovski","Adrian Vajiac","Sidy Danioko"]},{"key":"dc:creator","label":"Author","values":["Huang, Minhao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Computational and Data Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["goodness-of-fit","Ljung-Box","multivariate","time series","Applied Statistics","Data Science","Longitudinal Data Analysis and Time Series","Multivariate Analysis","Statistical Methodology","Statistical Models"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.chapman.edu/cads_dissertations/44"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, multidimensional time series scenarios. We use large sample simulation data for a range of values of sample sizes, lags, and number of time series to obtain an empirical estimation of the correct rejection regions for the particular combination of values of these variables. Furthermore, we use a regression modeling with interactions and covariate power combinations to parametrically extend these precise rejection regions to all combination of values of sample sizes, lags, and number of time series. Our results show that we attain almost perfect Type I error rates across all scenarios. These findings will improve the goodness-of-fit diagnostics for multivariate time series analysis.
"]},{"key":"dc:source","label":"Dc Source","values":["M. Huang, \"A novel correction for the multivariate Ljung-Box test,\" M. S. thesis, Chapman University, Orange, CA, 2024. https://doi.org/10.36837/chapman.000568"]},{"key":"dc:title","label":"Title","values":["A Novel Correction for the Multivariate Ljung-Box Test"]}]}],"canonical_facts":{"dc:contributor":["Cyril Rakovski","Adrian Vajiac","Sidy Danioko"],"dc:creator":["Huang, Minhao"],"dc:description.abstract":["This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, multidimensional time series scenarios. We use large sample simulation data for a range of values of sample sizes, lags, and number of time series to obtain an empirical estimation of the correct rejection regions for the particular combination of values of these variables. Furthermore, we use a regression modeling with interactions and covariate power combinations to parametrically extend these precise rejection regions to all combination of values of sample sizes, lags, and number of time series. Our results show that we attain almost perfect Type I error rates across all scenarios. These findings will improve the goodness-of-fit diagnostics for multivariate time series analysis.
"],"dc:identifier":["https://digitalcommons.chapman.edu/cads_dissertations/44"],"dc:source":["M. Huang, \"A novel correction for the multivariate Ljung-Box test,\" M. S. thesis, Chapman University, Orange, CA, 2024. https://doi.org/10.36837/chapman.000568"],"dc:subject":["goodness-of-fit","Ljung-Box","multivariate","time series","Applied Statistics","Data Science","Longitudinal Data Analysis and Time Series","Multivariate Analysis","Statistical Methodology","Statistical Models"],"dc:title":["A Novel Correction for the Multivariate Ljung-Box Test"],"thesis:degree_discipline":["Computational and Data Sciences"],"thesis:degree_level":["Thesis"]},"updated_at":"2026-07-24T01:38:37Z"}