Multivariate Wold Decompositions

Simone Cerreia-Vioglio, Fulvio Ortu, Federico Severino and Claudio Tebaldi

No 606, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: The Wold decomposition of a weakly stationary time series extends to the multivariate case by allowing each entry of a weakly stationary vectorial process to linearly depend on the components of a vector of shocks. Since univariate coefficients are replaced by matrices, we propose a modelling approach based on Hilbert A-modules defined over the algebra of squared matrices. The Abstract Wold Theorem for Hilbert A-modules, that we prove, delivers two orthogonal decompositions of vectorial processes: the Multivariate Classical Wold Decomposition, which exploits the lag operator as isometry, and the Multivariate Extended Wold Decomposition, where a scaling operator is employed. The latter enables us to disentangle the heterogeneous levels of persistence of a weakly stationary vectorial process. Hence, the persistent components of the macro-financial variables into consideration are related to the overlapping of different sources of randomness with specific persistence. We finally provide a simple application to V AR models.

Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://repec.unibocconi.it/igier/igi/wp/2017/606.pdf (application/pdf)

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:igi:igierp:606

Ordering information: This working paper can be ordered from
https://repec.unibocconi.it/igier/igi/

Access Statistics for this paper

More papers in Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University via Rontgen, 1 - 20136 Milano (Italy).
Bibliographic data for series maintained by ().