### 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 |
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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 Jan 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability