Nonparametric Approach for Non-Gaussian Vector Stationary Processes

Masanobu Taniguchi, Madan L. Puri and Masao Kondo

Journal of Multivariate Analysis, 1996, vol. 56, issue 2, 259-283

Abstract: Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf([lambda]). In this paper we consider the testing problemH: [integral operator][pi]-[pi] K{f([lambda])} d[lambda]=cagainstA: [integral operator][pi]-[pi] K{f([lambda])} d[lambda][not equal to]c, whereK{·} is an appropriate function andcis a given constant. For this problem we propose a testTnbased on [integral operator][pi]-[pi] K{f([lambda])} d[lambda]=c, wheref([lambda]) is a nonparametric spectral estimator off([lambda]), and we define an efficacy ofTnunder a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectraf4Zofz(t). If it does not depend onf4Z, we say thatTnis non-Gaussian robust. We will give sufficient conditions forTnto be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis off([lambda]). The essential point of our approach is that we do not assume the parametric form off([lambda]). Also some numerical studies are given and they confirm the theoretical results.

Keywords: non-Gaussian; vector; stationary; process; nonparametric; hypothesis; testing; spectral; density; matrix; fourth-order; cumulant; spectral; density; non-Gaussian; robustness; efficacy; measure; of; linear; dependence; principal; components; analysis; of; time; series; nonparametric; spectral; estimator; asymptotic; theory (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(96)90014-7
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:56:y:1996:i:2:p:259-283

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().