### 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 |
---|---|

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 |

### Fingerprint

### 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

### Cite this

*Journal of Time Series Analysis*,

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

**NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS.** / Taniguchi, Masanobu; Kondo, Masao.

Research output: Contribution to journal › Article

*Journal of Time Series Analysis*, vol. 14, no. 4, pp. 397-408. https://doi.org/10.1111/j.1467-9892.1993.tb00153.x

}

TY - JOUR

T1 - NON‐PARAMETRIC APPROACH IN TIME SERIES ANALYSIS

AU - Taniguchi, Masanobu

AU - Kondo, Masao

PY - 1993

Y1 - 1993

N2 - Abstract. Suppose that {Xt} 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{fn(Λ)}dΛ where fn(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.

AB - Abstract. Suppose that {Xt} 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{fn(Λ)}dΛ where fn(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.

KW - asymptotic relative efficiency

KW - Burg's entropy

KW - contiguous alternative

KW - efficacy

KW - exponential spectral model

KW - Gaussian stationary process

KW - Non‐parametric hypothesis testing

KW - non‐parametric spectral estimator

KW - spectral density

UR - http://www.scopus.com/inward/record.url?scp=84981411546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981411546&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9892.1993.tb00153.x

DO - 10.1111/j.1467-9892.1993.tb00153.x

M3 - Article

AN - SCOPUS:84981411546

VL - 14

SP - 397

EP - 408

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 4

ER -