Robinson, Peter
(1995)
*Gaussian semiparametric estimation of long range dependence.*
Annals of Statistics, 23 (5).
pp. 1630-1661.
ISSN 0090-5364

## Abstract

Assuming the model f(A) GA1- 2H, as A -- 0 +, for the spectral densityo f a covariances tationaryp rocess,w e considera n estimateo f H E (0, 1) which maximizes an approximate form of frequency domain Gaussian likelihood, where discrete averaging is carried out over a neighbourhood of zero frequency which degenerates slowly to zero as sample size tends to infinityT. he estimate has several advantages. It is shown to be consistent under mild conditions. Under conditions which are not greatly stronger, it is shown to be asymptotically normal and more efficientt han previous estimates. Gaussianity is nowhere assumed in the asymptotict heory,t he limitingn ormal distributioni s of very simple form, involving a variance which is not dependent on unknown parameters, and the theory covers simultaneously the cases f(A) -x oc, f(A) -+ 0 and f(A) -+ C E (0, oc), as A -* 0. Monte Carlo evidence on finite-sample performance is reported, along with an application to a historical series of minimum levels of the River Nile.

Item Type: | Article |
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Official URL: | http://imstat.org/aos/ |

Additional Information: | © 1995 Institute of Mathematical Statistics |

Divisions: | Economics |

Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |

JEL classification: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods |

Sets: | Departments > Economics Collections > Economists Online |

Date Deposited: | 27 Apr 2007 |

Last Modified: | 30 Jan 2019 15:39 |

URI: | http://eprints.lse.ac.uk/id/eprint/1120 |

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