 Asymptotic Analysis of a Multiple Frequency Estimation MethodT. H. Li and B. Kedem Journal of Multivariate Analysis, 1993, vol. 46, issue 2, 214-236 Abstract: A recently proposed method of multiple frequency estimation for mixed-spectrum time series is analyzed. The so-called PF method is a procedure that combines the autoregressive (AR) representation of superimposed sinusoids with the idea of parametric filtering. The gist of the method is to parametrize a linear filter in accord with a certain parametrization property, as suggested by the particular form of the bias encountered by Prony's least-squares estimator for the AR model. It is shown that for any parametric filter with this property, the least-squares estimator obtained from the filtered data is almost surely contractive as a function of the filter parameter and has a unique multivariate fixed-point in the vicinity of the true AR parameter. The fixed-point, known as the PF estimator, is shown to be stronly consistent for estimating the AR model, and the chronic bias of Prony's estimator is thus eliminated. The almost sure convergence of an iterative algorithm that calculates the fixed-point and the asymptotic normality of the PF estimator are also established. The all-pole filter is considered as an example and application of the developed theory. Date: 1993 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:46:y:1993:i:2:p:214-236 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.