TitleMultivariate autoregressive modular processes
NameZhao, Xiang (author), Ben-Israel, Adi (chair), Prékopa, András (internal member), Boros, Endre (internal member), Melamed, Benjamin (internal member), Wardi, Yorai (outside member), Rutgers University, Graduate School - New Brunswick,
DescriptionThis 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.
NoteIncludes bibliographical references
Noteby Xiang Zhao
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.