### Abstract

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 T_{n} based on ∫^{π}_{-π} K{f̂_{n}(λ)} dλ, where f̂_{n}(λ) is a nonparametric spectral estimator of f(λ), and we define an efficacy of T_{n} under a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectra f^{Z}_{4} of z(t). If it does not depend on f^{Z}_{4}, we say that T_{n} is non-Gaussian robust. We will give sufficient conditions for T_{n} 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 language | English |
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Pages (from-to) | 259-283 |

Number of pages | 25 |

Journal | Journal of Multivariate Analysis |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1996 Feb |

Externally published | Yes |

### Keywords

- 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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## Cite this

*Journal of Multivariate Analysis*,

*56*(2), 259-283. https://doi.org/10.1006/jmva.1996.0014