### Abstract

Language | English |
---|---|

Title of host publication | Time Series Analysis |

Subtitle of host publication | Methods and Applications |

Editors | Tata Subba Rao |

Place of Publication | Amsterdam |

Publisher | Elsevier B.V. |

Pages | 157-186 |

Number of pages | 30 |

Volume | 30 |

ISBN (Print) | 978-0-444-53858-1 |

DOIs | |

Status | Published - 2012 |

### Publication series

Name | Handbook of Statistics |
---|---|

Volume | 30 |

ISSN (Print) | 0169-7161 |

### Fingerprint

### Cite this

*Time Series Analysis: Methods and Applications*(Vol. 30, pp. 157-186). (Handbook of Statistics; Vol. 30). Amsterdam: Elsevier B.V.. DOI: 10.1016/B978-0-444-53858-1.00007-7

**Functional Time Series.** / Hörmann, Siegfried; Kokoszka, Piotr P.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

*Time Series Analysis: Methods and Applications.*vol. 30, Handbook of Statistics, vol. 30, Elsevier B.V., Amsterdam, pp. 157-186. DOI: 10.1016/B978-0-444-53858-1.00007-7

}

TY - CHAP

T1 - Functional Time Series

AU - Hörmann,Siegfried

AU - Kokoszka,Piotr P.

N1 - DOI: 10.1016/B978-0-444-53858-1.00007-7

PY - 2012

Y1 - 2012

N2 - This chapter is an account of the recent research that deals with curves observed consecutively over time. The curves are viewed in the framework of functional data analysis, that is, each of them is considered as a whole statistical object. We describe the Hilbert space framework within which the mathematical foundations are developed. We then introduce the most popular model for such data, the functional autoregressive process, and discuss its properties. This is followed by the introduction of a general framework that quantifies the temporal dependence of curves. Within this framework, we discuss analogs of central concepts of time series analysis of scalar data, including the definition and the estimation of an analog of the long-run variance.

AB - This chapter is an account of the recent research that deals with curves observed consecutively over time. The curves are viewed in the framework of functional data analysis, that is, each of them is considered as a whole statistical object. We describe the Hilbert space framework within which the mathematical foundations are developed. We then introduce the most popular model for such data, the functional autoregressive process, and discuss its properties. This is followed by the introduction of a general framework that quantifies the temporal dependence of curves. Within this framework, we discuss analogs of central concepts of time series analysis of scalar data, including the definition and the estimation of an analog of the long-run variance.

U2 - 10.1016/B978-0-444-53858-1.00007-7

DO - 10.1016/B978-0-444-53858-1.00007-7

M3 - Chapter

SN - 978-0-444-53858-1

VL - 30

T3 - Handbook of Statistics

SP - 157

EP - 186

BT - Time Series Analysis

PB - Elsevier B.V.

CY - Amsterdam

ER -