TY - JOUR

T1 - Nonparametric approach for non-gaussian vector stationary processes

AU - Taniguchi, Masanobu

AU - Puri, Madan L.

AU - Kondo, Masao

N1 - Funding Information:
Received September 8, 1994. AMS 1980 subject classifications: primary 62M15, 62G10. Key words and phrases: 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. * Research supported by the Office of Naval Research Contract N00014-91-J-1020.

PY - 1996/2

Y1 - 1996/2

N2 - Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrix f(λ). In this paper we consider the testing problem H:∫π-π K{f(λ)} dλ = c against A: ∫π-π K{f(λ)} dλ ≠ c, where K{·} is an appropriate function and c is a given constant. For this problem we propose a test Tn based on ∫π-π K{f̂n(λ)} dλ, where f̂n(λ) is a nonparametric spectral estimator of f(λ), and we define an efficacy of Tn under a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectra fZ4 of z(t). If it does not depend on fZ4, we say that Tn is non-Gaussian robust. We will give sufficient conditions for Tn to 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 of f(λ). The essential point of our approach is that we do not assume the parametric form of f(λ). Also some numerical studies are given and they confirm the theoretical results.

AB - Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrix f(λ). In this paper we consider the testing problem H:∫π-π K{f(λ)} dλ = c against A: ∫π-π K{f(λ)} dλ ≠ c, where K{·} is an appropriate function and c is a given constant. For this problem we propose a test Tn based on ∫π-π K{f̂n(λ)} dλ, where f̂n(λ) is a nonparametric spectral estimator of f(λ), and we define an efficacy of Tn under a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectra fZ4 of z(t). If it does not depend on fZ4, we say that Tn is non-Gaussian robust. We will give sufficient conditions for Tn to 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 of f(λ). The essential point of our approach is that we do not assume the parametric form of f(λ). Also some numerical studies are given and they confirm the theoretical results.

KW - Analysis of time series

KW - Efficacy

KW - Fourth-order cumulant spectral density

KW - Measure of linear dependence

KW - Non-Gaussian robustness

KW - Non-Gaussian vector stationary process

KW - Nonparametric hypothesis testing

KW - Principal components

KW - Spectral density matrix

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U2 - 10.1006/jmva.1996.0014

DO - 10.1006/jmva.1996.0014

M3 - Article

AN - SCOPUS:0030077092

VL - 56

SP - 259

EP - 283

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 2

ER -