Asymptotic normality of wavelet estimators of the memory parameter for linear processes

F. Roueff and M. S. Taqqu

Journal of Time Series Analysis, 2009, vol. 30, issue 5, 534-558

Abstract: Abstract. We consider linear processes, not necessarily Gaussian, with long, short or negative memory. The memory parameter is estimated semi‐parametrically using wavelets from a sample X1,…, Xn of the process. We treat both the log‐regression wavelet estimator and the wavelet Whittle estimator. We show that these estimators are asymptotically normal as the sample size n → ∞ and we obtain an explicit expression for the limit variance. These results are derived from a general result on the asymptotic normality of the scalogram for linear processes, conveniently centred and normalized. The scalogram is an array of quadratic forms of the observed sample, computed from the wavelet coefficients of this sample. In contrast to quadratic forms computed on the basis of Fourier coefficients such as the periodogram, the scalogram involves correlations which do not vanish as the sample size n → ∞.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9892.2009.00627.x

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:30:y:2009:i:5:p:534-558

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 ().