EFFICIENT NON-PARAMETRIC ESTIMATION OF THE SPECTRAL DENSITY IN THE PRESENCE OF MISSING OBSERVATIONS

Sam Efromovich

Journal of Time Series Analysis, 2014, vol. 35, issue 5, 407-427

Abstract: type="main" xml:id="jtsa12072-abs-0001"> The problem of non-parametric spectral density estimation for discrete-time series in the presence of missing observations has a long history. In particular, the first consistent estimators of the spectral density have been developed at about the same time as consistent estimators for non-parametric regression. On the other hand, while for now, the theory of efficient (under the minimax mean integrated squared error criteria) and adaptive nonparametric regression estimation with missing data is well developed, no similar results have been proposed for the spectral density of a time series whose observations are missed according to an unknown stochastic process. This article develops the theory of efficient and adaptive estimation for a class of spectral densities that includes classical causal autoregressive moving-average time series. The developed theory shows how a missing mechanism affects the estimation and what penalty it imposes on the risk convergence. In particular, given costs of a single observation in time series with and without missing data and a desired accuracy of estimation, the theory allows one to choose the cost-effective time series. A numerical study confirms the asymptotic theory.

Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1111/jtsa.12072 (text/html)
Access to full text is restricted to subscribers.

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:35:y:2014:i:5:p:407-427

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 ().