Nonparametric approach for non-gaussian vector stationary processes

Masanobu Taniguchi*, Madan L. Puri, Masao Kondo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


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 K{f(λ)} dλ = c against A: ∫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 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.

Original languageEnglish
Pages (from-to)259-283
Number of pages25
JournalJournal of Multivariate Analysis
Issue number2
Publication statusPublished - 1996 Feb
Externally publishedYes


  • Analysis of time series
  • Efficacy
  • Fourth-order cumulant spectral density
  • Measure of linear dependence
  • Non-Gaussian robustness
  • Non-Gaussian vector stationary process
  • Nonparametric hypothesis testing
  • Principal components
  • Spectral density matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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