The k-th Power Expectile Periodogram for Time Series Analysis

The k-th Power Expectile Periodogram for Time Series Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The k-th Power Expectile Periodogram for Time Series Analysis Tianbo Chen, Ta-Hsin Li, Wenzhi Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9062860/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract This paper introduces the k-th power expectile periodogram (KEP) as a generalization of the quantile periodogram (QP) and expectile periodogram (EP) for time series analysis. Constructed from trigonometric k-th power expectile regression (KER), the KEP provides a flexible tool to balance robustness and efficiency. The KEP retains the key properties of the ordinary periodogram as a frequency-domain representation of serial dependence in time series, while offering a more comprehensive understanding by examining the data across the entire range of expectile levels with power 1 < k ≤ 2. Simulations demonstrate the capability of the KEP in detecting hidden periodicities, while maintaining robustness against outliers. We establish the asymptotic theory and investigate the relationship between the KEP and the so-called k-th power expectile spectrum (KES). Finally, we leverage the inherent two-dimensional property of the KEP to train a convolutional neural network (CNN) to classify the epilepsy electroencephalogram (EEG) data, where the proposed estimator outperforms competitive estimators. k-th Power expectile regression Hidden periodicity Periodogram Time series analysis Spectral analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 25 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers invited by journal 12 Apr, 2026 Editor assigned by journal 09 Mar, 2026 Submission checks completed at journal 09 Mar, 2026 First submitted to journal 08 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9062860","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":623361271,"identity":"7d116b92-97b8-4641-98dc-484d9930435b","order_by":0,"name":"Tianbo Chen","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Tianbo","middleName":"","lastName":"Chen","suffix":""},{"id":623361272,"identity":"e7bb105e-e1fc-4cf7-b491-e5e2f343c47a","order_by":1,"name":"Ta-Hsin Li","email":"","orcid":"","institution":"IBM Research - Thomas J. Watson Research Center","correspondingAuthor":false,"prefix":"","firstName":"Ta-Hsin","middleName":"","lastName":"Li","suffix":""},{"id":623361273,"identity":"58878999-2c70-44ad-9542-099b4144487b","order_by":2,"name":"Wenzhi Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYPACGwYDEMVDgpY00rUcJkGLwfkzhp8Lfp2XN5dIYHzwto1B3pyglgNnjKVn9t023DkjgdlwbhuD4c4GAlrMDvYYSPP23GbccCOBTZq3jSHB4AAhLYd5jH/z9pyzB2ph/02clmM8ZtI8Pw4kgmxhJkqL/Rm2MmvehuTkDWceNkvOOSdhuIGQFsn+w5tv8/yxs91wPPnghzdlNvIEbWFg4DBgYGwDMRgbgIQEQfVAwP6AgeEPMQpHwSgYBaNgxAIAhDlBsK7SmUEAAAAASUVORK5CYII=","orcid":"","institution":"Anhui University","correspondingAuthor":true,"prefix":"","firstName":"Wenzhi","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2026-03-08 08:23:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9062860/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9062860/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107270354,"identity":"f6f4a005-d819-4fd9-89ac-d53792dcd1c4","added_by":"auto","created_at":"2026-04-19 17:56:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1053169,"visible":true,"origin":"","legend":"","description":"","filename":"KEP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9062860/v1_covered_0b6a9e32-515a-4bb9-b3e7-5325ef4517f7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eThe k-th Power Expectile Periodogram for Time Series Analysis\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"k-th Power expectile regression, Hidden periodicity, Periodogram, Time series analysis, Spectral analysis","lastPublishedDoi":"10.21203/rs.3.rs-9062860/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9062860/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces the k-th power expectile periodogram (KEP) as a generalization of the quantile periodogram (QP) and expectile periodogram (EP) for time series analysis. Constructed from trigonometric k-th power expectile regression (KER), the KEP provides a flexible tool to balance robustness and efficiency. The KEP retains the key properties of the ordinary periodogram as a frequency-domain representation of serial dependence in time series, while offering a more comprehensive understanding by examining the data across the entire range of expectile levels with power 1 \u0026lt; k ≤ 2. Simulations demonstrate the capability of the KEP in detecting hidden periodicities, while maintaining robustness against outliers. We establish the asymptotic theory and investigate the relationship between the KEP and the so-called k-th power expectile spectrum (KES). Finally, we leverage the inherent two-dimensional property of the KEP to train a convolutional neural network (CNN) to classify the epilepsy electroencephalogram (EEG) data, where the proposed estimator outperforms competitive estimators.\u003c/p\u003e","manuscriptTitle":"The k-th Power Expectile Periodogram for Time Series Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-19 17:56:09","doi":"10.21203/rs.3.rs-9062860/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-25T15:15:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"49862413961894046638990025819759595984","date":"2026-04-15T05:53:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"54538381453380964185115199129030586449","date":"2026-04-14T17:57:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-13T01:51:23+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-10T00:41:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-09T08:48:10+00:00","index":"","fulltext":""},{"type":"submitted","content":"Statistics and Computing","date":"2026-03-08T08:16:03+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"eb08d72d-5d2c-420d-a4e1-bbb6ed1bee01","owner":[],"postedDate":"April 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-19T17:56:09+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-19 17:56:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9062860","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9062860","identity":"rs-9062860","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}