Holighi, Khalil Shafie

Committee Member

Yu, Han

Committee Member

Khaledi, Bahaedin

Committee Member

Robinson, Jason D.


College of Education and Behavioral Science; School of Educational Research Leadership and Technology, Department of Applied Statistics and Research Methods


University of Northern Colorado

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Greeley, (Colo.)


University of Northern Colorado

Date Created



90 pages

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Born digital


In multivariate time series analysis, a Vector Autoregressive Moving Average model would be fitted to the data. Then, diagnostic checking methods are used to assess the goodness of fit for the fitted model. Different multivariate Portmanteau goodness of fit tests had been proposed for multivariate time series analysis. However, these previous tests suffer from low power in many situations, such as small sample sizes. To overcome this, a modified measure of autocorrelation was recently proposed by Fisher and Robbins (2018) using a logarithmic transformation of the determinant of a Toeplitz matrix that contains the multivariate correlations matrices. This new measure of serial correlation improves the power performance of the goodness of fit test statistic while maintaining the same asymptotic distribution under the null hypothesis. In this dissertation, we proposed two Portmanteau test statistics that employ the determinant and the trace of a Toeplitz matrix containing the improved measure of correlation. The asymptotic distributions of each presented test statistic was derived. Also, a simulation study was provided to explore the power performance of the proposed Portmanteau tests. A Monte Carlo method was used to calculate the empirical power in this simulation study. The new trace-based Portmanteau test statistic offered improvements in the power performance over existing tests. On the other hand, the determinant-based test statistic showed good power behavior in the case of moderate and large sample sizes.

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