Multivariate autoregressive modular processes

by Xiang Zhao

Institution: Rutgers University
Department: Operations Research
Degree: PhD
Year: 2010
Keywords: Multivariate analysis; Stochastic processes
Record ID: 1883502
Full text PDF: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000053224


This thesis defines a new class of vector-valued stochastic processes, called MARM (Multivariate Autoregressive Modular) Processes. It describes the construction of two flavors of MARM processes, MARM+ and MARM−, studies the statistics of MARM processes (transition structure and second order statistics), and devises MARM-based fitting and forecasting algorithms providing point estimators and confidence intervals. The key advantage of MARM processes is their ability to fit a strong statistical signature consisting of empirical first-order and second-order statistics simultaneously. More precisely, MARM processes exactly fit arbitrary multi-dimensional empirical histograms and approximately fit the leading empirical autocorrelations and cross-correlations functions. This ability appears to make the MARM modeling methodology unique in its goal of fitting a model to such a class of strong statistical signatures. Furthermore, the thesis proposes practical MARM modeling and forecasting methodologies of considerable generality, suitable for implementation on a computer. We demonstrate the efficacy of these methodologies with an example of a three-dimension time series vector, using a software environment, called MultiArmLab, which supports MARM modeling and forecasting. Includes abstract