Date of Award

Spring 5-2024

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational and Data Sciences

First Advisor

Cyril Rakovski

Second Advisor

Adrian Vajiac

Third Advisor

Sidy Danioko


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.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.



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