### Abstract

Semiparametric estimation of long memory refers to periodogram based estimation of the shape of the spectral density f(λ) at low frequencies, where all but the lowest harmonics of the periodogram are discarded, so as to forego specification of the short range dynamic structure of the time series, and avoid bias incurred when the latter is misspecified. Such a procedure entails an order of magnitude loss of efficiency with respect to parametric estimation, but may be warranted when long series (earth scientific or financial) can be obtained. This paper presents strategies proposed for the choice of bandwidth, i.e. the number of periodogram harmonics used in estimation, with the aim of minimizing this loss of efficiency. Such strategies are assessed with respect to minimax rates of convergence, that depend on the smoothness of |λ|^{-2d} f(λ) (where d is the long memory parameter) in the neighbourhood of frequency zero. The plug-in strategy is discussed in the case where the degree of local smoothness is known a priori, and adaptive estimation of d is discussed for the case where the degree of local smoothness is unknown.

Original language | English (US) |
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Title of host publication | Long Memory in Economics |

Publisher | Springer Berlin Heidelberg |

Pages | 157-172 |

Number of pages | 16 |

ISBN (Print) | 354022394X, 9783540226949 |

DOIs | |

State | Published - Dec 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)

### Cite this

*Long Memory in Economics*(pp. 157-172). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-34625-8_6

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*Long Memory in Economics.*Springer Berlin Heidelberg, pp. 157-172. https://doi.org/10.1007/978-3-540-34625-8_6

**Bandwidth choice, optimal rates and adaptivity in semiparametric estimation of long memory.** / Henry, Marc.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Bandwidth choice, optimal rates and adaptivity in semiparametric estimation of long memory

AU - Henry, Marc

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Semiparametric estimation of long memory refers to periodogram based estimation of the shape of the spectral density f(λ) at low frequencies, where all but the lowest harmonics of the periodogram are discarded, so as to forego specification of the short range dynamic structure of the time series, and avoid bias incurred when the latter is misspecified. Such a procedure entails an order of magnitude loss of efficiency with respect to parametric estimation, but may be warranted when long series (earth scientific or financial) can be obtained. This paper presents strategies proposed for the choice of bandwidth, i.e. the number of periodogram harmonics used in estimation, with the aim of minimizing this loss of efficiency. Such strategies are assessed with respect to minimax rates of convergence, that depend on the smoothness of |λ|-2d f(λ) (where d is the long memory parameter) in the neighbourhood of frequency zero. The plug-in strategy is discussed in the case where the degree of local smoothness is known a priori, and adaptive estimation of d is discussed for the case where the degree of local smoothness is unknown.

AB - Semiparametric estimation of long memory refers to periodogram based estimation of the shape of the spectral density f(λ) at low frequencies, where all but the lowest harmonics of the periodogram are discarded, so as to forego specification of the short range dynamic structure of the time series, and avoid bias incurred when the latter is misspecified. Such a procedure entails an order of magnitude loss of efficiency with respect to parametric estimation, but may be warranted when long series (earth scientific or financial) can be obtained. This paper presents strategies proposed for the choice of bandwidth, i.e. the number of periodogram harmonics used in estimation, with the aim of minimizing this loss of efficiency. Such strategies are assessed with respect to minimax rates of convergence, that depend on the smoothness of |λ|-2d f(λ) (where d is the long memory parameter) in the neighbourhood of frequency zero. The plug-in strategy is discussed in the case where the degree of local smoothness is known a priori, and adaptive estimation of d is discussed for the case where the degree of local smoothness is unknown.

UR - http://www.scopus.com/inward/record.url?scp=84892236004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892236004&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-34625-8_6

DO - 10.1007/978-3-540-34625-8_6

M3 - Chapter

AN - SCOPUS:84892236004

SN - 354022394X

SN - 9783540226949

SP - 157

EP - 172

BT - Long Memory in Economics

PB - Springer Berlin Heidelberg

ER -