Does White Noise Dream of Square Waves? A Matching Pursuit Conundrum

Peter F. Craigmile (), Donald B. Percival () and Barry G. Quinn ()
Additional contact information
Peter F. Craigmile: CUNY, Hunter College
Donald B. Percival: University of Washington
Barry G. Quinn: Macquarie University

A chapter in Time Series and Wavelet Analysis, 2024, pp 199-220 from Springer

Abstract: Abstract Matching pursuit is a greedy model selection algorithm used to extract a possible signal that underlies a time series of interest. The method represents the series as a linear combination of vectors from a large collection of vectors (a dictionary) by incrementally adding the vector that reduces the residual sum of squares in a linear model. In this article it is demonstrated that the probability of selecting vectors from the dictionary need not be uniform when there is no underlying structure in the series of interest and when the vectors in the dictionary are highly correlated. In particular, via simulation studies and analytic calculations, it is shown that matching pursuit can preferentially select square waves over sinusoids when analyzing Gaussian white noise, in some cases with a preference exceeding 95%. The ramification of this non-uniform selection is demonstrated for a climatological example, in which the scientific question is to explore underlying structures inherent in North Pacific indices.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-3-031-66398-7_10

Ordering information: This item can be ordered from
http://www.springer.com/9783031663987

DOI: 10.1007/978-3-031-66398-7_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().