### Abstract

Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.

Original language | English |
---|---|

Pages (from-to) | 142-158 |

Number of pages | 17 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Integral functional
- Periodogram
- Sequential interval estimation
- Sequential point estimation
- Spectral density
- Stationary process

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

**Sequential estimation for a functional of the spectral density of a Gaussian stationary process.** / Shiohama, Takayuki; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Annals of the Institute of Statistical Mathematics*, vol. 53, no. 1, pp. 142-158. https://doi.org/10.1023/A:1017976706781

}

TY - JOUR

T1 - Sequential estimation for a functional of the spectral density of a Gaussian stationary process

AU - Shiohama, Takayuki

AU - Taniguchi, Masanobu

PY - 2001

Y1 - 2001

N2 - Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.

AB - Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.

KW - Integral functional

KW - Periodogram

KW - Sequential interval estimation

KW - Sequential point estimation

KW - Spectral density

KW - Stationary process

UR - http://www.scopus.com/inward/record.url?scp=2142787920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142787920&partnerID=8YFLogxK

U2 - 10.1023/A:1017976706781

DO - 10.1023/A:1017976706781

M3 - Article

AN - SCOPUS:2142787920

VL - 53

SP - 142

EP - 158

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -