RATE OPTIMAL SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF THE GAUSSIAN TIME SERIES WITH LONG‐RANGE DEPENDENCE

Liudas Giraitis, Peter M. Robinson and Alexander Samarov

Journal of Time Series Analysis, 1997, vol. 18, issue 1, 49-60

Abstract: There exist several estimators of the memory parameter in long‐ memory time series models with the spectrum specified only locally near zero frequency. In this paper we give an asymptotic lower bound for the minimax risk of any estimator of the memory parameter as a function of the degree of local smoothness of the spectral density at zero. The lower bound allows one to evaluate and compare different estimators by their asymptotic behaviour, and to claim the rate optimality for any estimator attaining the bound. A log‐periodogram regression estimator, analysed by Robinson (Log‐periodogram regression of time series with long range dependence. Ann. Stat. 23 (1995), 1048‐‐72), is then shown to attain the lower bound, and is thus rate optimal.

Date: 1997
References: Add references at CitEc
Citations: View citations in EconPapers (35)

Downloads: (external link)
https://doi.org/10.1111/1467-9892.00038

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:18:y:1997:i:1:p:49-60

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by M.B. Priestley

More articles in Journal of Time Series Analysis from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().