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Topics in multivariate time series analysis: Statistical control, dimension reduction, visualization and their business applications
Abstract
Most business processes are, by nature, multivariate and autocorrelated. High-dimensionality is rooted in processes where more than one variable is considered simultaneously to provide a more comprehensive picture. Time series models are preferable to an independently identically distributed (I.I.D.) model because they capture the fact that many processes have a memory of their past. Examples of multivariate autocorrelation can be found in processes in the business fields such as Operations Management, Finance and Marketing. The topic of statistical control is most relevant to Quality Management. While both multivariate I.I.D. processes and univariate autocorrelated processes have received much attention in the Statistical Process Control (SPC) literature, little work has been done to simultaneously address high-dimensionality and autocorrelation. In this dissertation, this gap is filled by extending the univariate special cause chart and common cause chart to multivariate situations. In addition, two-chart control schemes are extended to nonstationary processes. Further, a class of Markov Chain models is proposed to provide accurate Average Run Length (ARL) computation when the process is autocorrelated. The second part of this dissertation aims to devise a dimension reduction method for autocorrelated processes. High-dimensionality often obscures the true underlying components of a process. In traditional multivariate literature, Principal Components Analysis (PCA) is the standard tool for dimension reduction. For autocorrelated processes, however, PCA fails to take into account the autocorrelation information. Thus, it is doubtful that PCA is the best choice. A two-step dimension reduction procedure is devised for multivariate time series. Comparisons based on both simulated examples and case studies show that the two-step procedure is more efficient in retrieving true underlying factors. Visualization of multivariate time series assists our understanding of the process. In the last part of this dissertation a simple three-dimensional graph is proposed to assist visualizing the results of PCA. It is intended to complement existing graphical methods for multivariate time series data. The idea is to visualize multivariate data as a surface that in turn can be decomposed with PCA. The developed surface plots are intended for statistical process analysis but may also help visualize economics data and, in particular, co-integration.
Subject Area
Management|Industrial engineering
Recommended Citation
Huang, Xuan, "Topics in multivariate time series analysis: Statistical control, dimension reduction, visualization and their business applications" (2010). Doctoral Dissertations Available from Proquest. AAI3409593.
https://scholarworks.umass.edu/dissertations/AAI3409593