### Abstract

Abstract. Suppose that {X_{t}} is a Gaussian stationary process with spectral density f(Λ). In this paper we consider the testing problem , where K(Λ) is an appropriate function and c is a given constant. This test setting is unexpectedly wide and can be applied to many problems in time series. For this problem we propose a test based on K{f_{n}(Λ)}dΛ where f_{n}(Λ) is a non‐parametric spectral estimator of f(Λ), and we evaluate the asymptotic power under a sequence of non‐parametric contiguous alternatives. We compare the asymptotic power of our test with the other and show some good properties of our test. It is also shown that our testing problem can be applied to testing for independence. Finally some numerical studies are given for a sequence of exponential spectral alternatives. They confirm the theoretical results and the goodness of our test.

Original language | English |
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Pages (from-to) | 397-408 |

Number of pages | 12 |

Journal | Journal of Time Series Analysis |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

### Keywords

- asymptotic relative efficiency
- Burg's entropy
- contiguous alternative
- efficacy
- exponential spectral model
- Gaussian stationary process
- Non‐parametric hypothesis testing
- non‐parametric spectral estimator
- spectral density

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

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## Cite this

*Journal of Time Series Analysis*,

*14*(4), 397-408. https://doi.org/10.1111/j.1467-9892.1993.tb00153.x