Wiener–Kolmogorov Filtering and Smoothing for Multivariate Series With State–Space Structure

Víctor Gómez

Journal of Time Series Analysis, 2007, vol. 28, issue 3, 361-385

Abstract: Abstract. Wiener–Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi‐infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state–space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener–Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/j.1467-9892.2006.00514.x

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:bla:jtsera:v:28:y:2007:i:3:p:361-385

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by M.B. Priestley

More articles in Journal of Time Series Analysis from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().