{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T11:34:22Z","timestamp":1779276862335,"version":"3.51.4"},"reference-count":34,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an \n            <jats:italic>Extended Wold Decomposition<\/jats:italic> based on an isometric \n            <jats:italic>scaling operator<\/jats:italic> that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence\u2010based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determinants of the variability of economic and financial time series.\n          <\/jats:p>","DOI":"10.3982\/qe994","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:51:29Z","timestamp":1580111489000},"page":"203-230","source":"Crossref","is-referenced-by-count":27,"title":["A persistence\u2010based Wold\u2010type decomposition for stationary time series"],"prefix":"10.3982","volume":"11","author":[{"given":"Fulvio","family":"Ortu","sequence":"first","affiliation":[{"name":"Department of Finance, Universit\u00e0 Bocconi"},{"name":"IGIER"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Severino","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Finance, Assurance et Immobilier, FSA, Universit\u00e9 Laval"},{"name":"Department of Economics, USI Lugano"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Tamoni","sequence":"additional","affiliation":[{"name":"Department of Finance and Economics, Rutgers Business School"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudio","family":"Tebaldi","sequence":"additional","affiliation":[{"name":"Department of Finance, Universit\u00e0 Bocconi"},{"name":"IGIER"},{"name":"Baffi-CAREFIN"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"key":"quan200067-bib-0001","doi-asserted-by":"crossref","DOI":"10.1887\/0750306920","volume-title":"The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance","author":"Addison","year":"2002"},{"issue":"3","key":"quan200067-bib-0002","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1111\/j.1540-6261.1997.tb02722.x","volume":"52","author":"Andersen","year":"1997","journal-title":"The Journal of Finance"},{"issue":"2","key":"quan200067-bib-0003","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1111\/1468-0262.00418","volume":"71","author":"Andersen","year":"2003","journal-title":"Econometrica"},{"issue":"8","key":"quan200067-bib-0004","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1016\/j.jfa.2009.08.011","volume":"258","author":"Baggett","year":"2010","journal-title":"Journal of Functional Analysis"},{"key":"quan200067-bib-0005","unstructured":"Bandi, F., A. 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