Statistics – Methodology
Scientific paper
2010-06-17
Statistics
Methodology
24 pages, 7 figures
Scientific paper
In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis implications, in what concerns separation of components, SSA forecasting and related signal parameter estimation methods. The roots of the characteristic polynomial for an LRF comprise the signal roots, which determine the structure of the time series, and extraneous roots. We show how the separability of two time series can be characterized in terms of their signal roots. All possible cases of exact separability are enumerated. We also examine properties of extraneous roots of the LRF used in SSA forecasting algorithms, which is equivalent to the Min-Norm vector in subspace-based estimation methods. We apply recent theoretical results for orthogonal polynomials on the unit circle, which enable us to precisely describe the asymptotic distribution of extraneous roots relative to the position of the signal roots.
No associations
LandOfFree
On signal and extraneous roots in Singular Spectrum Analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On signal and extraneous roots in Singular Spectrum Analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On signal and extraneous roots in Singular Spectrum Analysis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-551726