{"paper_id":"48b05df5-001e-478a-9cd9-4fe103c51b92","body_text":"On periodic log GARCH model with empirical application | 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 On periodic log GARCH model with empirical application Abdelouahab BIBI, Fayçal HAMDI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3975303/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract This article introduces a new class of volatility models known as Periodic log-Generalized Autoregressive Conditional Heteroscedastic ( P − log GARCH ) models, which incorporate periodic variations in the coefficients. These parameter variations are particularly relevant when incorporating seasonality into economic decision-making theory. The P − log GARCH formulation exhibits desirable properties, such as unconstrained positivity of parameters, absence of extreme value clustering, and a volatility trend. Specifically, the proposed model, without a trend, demonstrates periodic stationarity and is well-suited for data characterized by robust seasonal volatility. We investigate the probabilistic structure of this model and establish necessary and sufficient conditions for the existence of stationary solutions in a periodic sense. Additionally, we examine the strong consistency and asymptotic normality of the generalized quasi-maximum likelihood estimator ( GQMLE ) under mild assumptions. To assess the performance of our model, we conduct a Monte Carlo study to examine the finite-sample properties of the GQMLE . Finally, we present empirical evidence by applying the P − log GARCH model to analyze the exchange rates of the Algerian Dinar against the U.S. dollar and the Euro, thereby demonstrating its practical utility. MSC Classification : 62G20 , 62M10 Periodic log GARCH model Strict periodic stationarity Generalized QMLE Strong consistency Asymptotic normality Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 01 May, 2024 Reviews received at journal 24 Apr, 2024 Reviews received at journal 07 Apr, 2024 Reviewers agreed at journal 06 Apr, 2024 Reviewers agreed at journal 10 Mar, 2024 Reviewers invited by journal 07 Mar, 2024 Editor assigned by journal 25 Feb, 2024 Submission checks completed at journal 22 Feb, 2024 First submitted to journal 21 Feb, 2024 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. 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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-3975303\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":274320465,\"identity\":\"1ffb2ac7-69ef-46f6-96c4-8ae026568c13\",\"order_by\":0,\"name\":\"Abdelouahab BIBI\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYDACCQYDZgaDAzz8IE5CASlaJBtAWgyI1sJwAKgLxCNGC//s5g3MBQV3ZIzPr0788MCAQZ5f7AABS+4cK2CeYfCMx+zG280SQIcZzpydQMCaGzkGzDwGh4Fazm4AaUkwuE1AizxMi/GMs5t/EKXFAKbFgL93G3G2GAL9chjkF4kbvNssEgwkCPtF7nbzxscFf+7Y8/ef3XzzR4WNPL80AS0gcABMSoBVShBWjgD8B0hRPQpGwSgYBSMJAAA2UkUObmlDegAAAABJRU5ErkJggg==\",\"orcid\":\"\",\"institution\":\"USTHB\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Abdelouahab\",\"middleName\":\"\",\"lastName\":\"BIBI\",\"suffix\":\"\"},{\"id\":274320466,\"identity\":\"e92b987b-3abe-4861-b81a-b87d6e4bea9c\",\"order_by\":1,\"name\":\"Fayçal HAMDI\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"USTHB\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Fayçal\",\"middleName\":\"\",\"lastName\":\"HAMDI\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-02-21 11:16:23\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-3975303/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-3975303/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s11222-024-10532-3\",\"type\":\"published\",\"date\":\"2024-11-13T15:57:39+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":69285962,\"identity\":\"8a7657f8-cc79-4f5a-9ec7-a25a8b4de5c6\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 19:28:49\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":872511,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-3975303/v1_covered_a900d62e-2b20-43c9-afe6-31a332b6c398.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"On periodic log GARCH model with empirical application\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"Periodic log GARCH model, Strict periodic stationarity, Generalized QMLE, Strong consistency, Asymptotic normality\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-3975303/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-3975303/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThis article introduces a new class of volatility models known as Periodic log-Generalized Autoregressive Conditional Heteroscedastic (\\u003cem\\u003e\\u003cstrong\\u003eP − \\u003c/strong\\u003e\\u003c/em\\u003e\\u003cstrong\\u003elog \\u003c/strong\\u003e\\u003cem\\u003e\\u003cstrong\\u003eGARCH\\u003c/strong\\u003e\\u003c/em\\u003e) models, which incorporate periodic variations in the coefficients. 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