GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS IN MODEL ANALYSIS

Eugene V. Dulov (), Humberto Sarria Zapata () and Natalia A. Andrianova ()
Additional contact information
Eugene V. Dulov: Departamento de Mathematicas, Facultad de Ciencias, Universidad Nacional de Colombia, Bogota, Colombia
Humberto Sarria Zapata: Departamento de Mathematicas, Facultad de Ciencias, Universidad Nacional de Colombia, Bogota, Colombia
Natalia A. Andrianova: Department of Mathematics and Mechanics, Ulyanovsk State University, 432700, Leo Tolstoy St., 42, Ulyanovsk, Russia

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 02, 171-184

Abstract: For a variety of processes we can observe and register their characteristics, making up a sequence of measurement vectors or matrices (rectangular in general). Our goal is to extract some model dependent information using the available information. Such approaches are typical in technology (for a neat chemistry example, see [7,9]) and model analysis like parameter identification of linear stochastic dynamic systems. Since a stochastic nature of financial and economic data is evident, we can extend this data analysis technique to a number of new applications.If we are successful, some kind of adaptive filter can be further constructed (similar to the classic Kalman's one, for example). Inspired with formal model parameters, we can apply this filter to process financial data like stock information to predict and verify how close is a mathematical model to a real-time data.Namely, when provided with a set measurements represented by matrices Ai ∈ Mm,n(ℝ), we have to estimate a problem dependent characteristic matrices \[ \min_{r,P,B_1,\ldots,B_k,Q}\sum_{i=1}^k \|A_i-PB_iQ^T\|_F^2, \] with P,Q being orthonormal matrices, Bi ∈ Mr(ℝ), r ≤ min{m,n}. Formulated as above, the problem is usually called a generalized singular value decomposition (GSVD) problem and could be solved numerically [1, 2]. These matrices provide some basic information applicable for higher level automated problem solver or human interpretation.

Keywords: Generalized singular value decomposition; adaptive filtering; identification; data prediction (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024906003500
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:09:y:2006:i:02:n:s0219024906003500

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024906003500

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().