{"id":2,"date":"2024-12-02T08:16:00","date_gmt":"2024-12-02T08:16:00","guid":{"rendered":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/?page_id=2"},"modified":"2026-07-20T16:09:16","modified_gmt":"2026-07-20T15:09:16","slug":"my-research","status":"publish","type":"page","link":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/my-research\/","title":{"rendered":"My Research"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2\" class=\"elementor elementor-2\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c378945 e-flex e-con-boxed e-con e-parent\" data-id=\"c378945\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a00a3c7 elementor-widget elementor-widget-heading\" data-id=\"a00a3c7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Research<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ee90be7 e-flex e-con-boxed e-con e-parent\" data-id=\"ee90be7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7a4b0ed elementor-widget elementor-widget-heading\" data-id=\"7a4b0ed\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Dissertations<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-470d7d0 e-flex e-con-boxed e-con e-parent\" data-id=\"470d7d0\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9ce310a elementor-widget elementor-widget-heading\" data-id=\"9ce310a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-default\">MRes. In statistics and operational research (Lancaster University, 2025)<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-44193c2 elementor-widget elementor-widget-text-editor\" data-id=\"44193c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div style=\"text-align: left\"><strong>Supervisors: <\/strong><em>Israel Mart\u00ednez-Hern\u00e1ndez (Lancaster University), Emma Eastoe (Lancaster University), Wagner Barreto-Souza (University College Dublin)<\/em><\/div><div>\u00a0<\/div><div><strong>Description: <\/strong>PhD research proposal in a dissertation style. It explores novel research directions in (i) count time series and (ii) point processes. The objective of the dissertation is to have a solid literature review and strong initial steps to continue the research in the PhD phase.\u00a0<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-fa060c1 e-flex e-con-boxed e-con e-parent\" data-id=\"fa060c1\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-823dd36 elementor-widget elementor-widget-heading\" data-id=\"823dd36\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-default\">MSc.  in Probability and Statistics:   Partial Least Squares for non-stationary time series: A forecasting Approach (CIMAT, 2024)<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8968b2 elementor-widget elementor-widget-text-editor\" data-id=\"d8968b2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div style=\"text-align: left\"><strong>Supervisors: <\/strong><em>Graciela Gonz\u00e1lez-Far\u00edas (CIMAT),\u00a0 Israel Mart\u00ednez-Hern\u00e1ndez (Lancaster University)<\/em><\/div><div>\u00a0<\/div><div><strong>Description: <\/strong>This thesis presents a detailed study of the Partial Least Squares (PLS) method (Wold, 1966). An innovative generalisation of the PLS algorithm is proposed for the case in which both the response and explanatory variables are functional, so-called Functional PLS (FPLS). A novel methodology using FPLS and functional principal component analysis (FPCA) is explored to estimate a stable component of a non-stationary functional time series.\u00a0\u00a0<\/div><div>\u00a0<\/div><div><a href=\"http:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2026\/07\/thesis_compressed.pdf\" target=\"_blank\" rel=\"noopener\">Link to manuscript<\/a><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-eef476c e-flex e-con-boxed e-con e-parent\" data-id=\"eef476c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4b4219f elementor-widget elementor-widget-heading\" data-id=\"4b4219f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Publications<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-367ac86 e-flex e-con-boxed e-con e-parent\" data-id=\"367ac86\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-001798c elementor-widget elementor-widget-text-editor\" data-id=\"001798c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li>2025 Vasquez Martinez, R, Gonzalez Farias, G, Marquez Urbina, J U &amp; Corona, F. Over the Stability of a<br \/>Non-Stationary Multivariate Time Series. <a href=\"https:\/\/doi.org\/10.48550\/arXiv.2506.22407\" target=\"_blank\" rel=\"noopener\">doi:10.48550\/arXiv.2506.22407<\/a>.<\/li><li>2023 Gonzalez Farias, G, Vasquez Martinez, R, Marquez Urbina, J U&amp; Ramos Quiroga, R. A Gompertz<br \/>Mixture Approach for Modeling the Evolution of the COVID-19 Dynamics. Revista de Matem\u00e1tica: Teor\u00eda y Aplicaciones. <a href=\"https:\/\/archivo.revistas.ucr.ac.cr\/\/index.php\/matematica\/article\/view\/50927\" target=\"_blank\" rel=\"noopener\">doi:10.15517\/rmta.v30i1.50927<\/a>.<\/li><li>2022 Vasquez Martinez, R, Villarreal Haro, K, Sanchez Leon, C A, Ortiz Arana, E I, Cardenas Trevi\u00f1o, J<br \/>A&amp; Martin, Gonzalez, E M. Conditional Passing Times for Cramer-Lundberg Risk Model. Jovenes en la<br \/>Ciencia 16. <a href=\"https:\/\/www.jovenesenlaciencia.ugto.mx\/index.php\/jovenesenlaciencia\/article\/view\/3659\">Link<\/a><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5421f74 e-flex e-con-boxed e-con e-parent\" data-id=\"5421f74\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f63b61b elementor-widget elementor-widget-heading\" data-id=\"f63b61b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">TALKS<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9add1e7 e-flex e-con-boxed e-con e-parent\" data-id=\"9add1e7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8a20eb2 elementor-widget elementor-widget-text-editor\" data-id=\"8a20eb2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><strong>&#8220;Modelling Complex Dependency Structures in Count Time Series&#8221;\u00a0<\/strong>at CIMAT&#8217;s Probability and Statistics students&#8217; talks (<a href=\"https:\/\/sites.google.com\/cimat.mx\/seminariopepe?usp=sharing\" target=\"_blank\" rel=\"noopener\">PEPE<\/a>). March 2026.\u00a0<\/li><li><strong>&#8220;Gompertz Mixture with covariables for modeling COVID-19 pandemic&#8221;\u00a0<\/strong>at <a href=\"https:\/\/cimpa.ucr.ac.cr\/\">CIMPA<\/a>&#8216;s Seminar. <em>November 2023<\/em>.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b57eb7f e-grid e-con-boxed e-con e-parent\" data-id=\"b57eb7f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3f8abe6 elementor-widget elementor-widget-image\" data-id=\"3f8abe6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"688\" height=\"688\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/poster_crop.png\" class=\"attachment-large size-large wp-image-250\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/poster_crop.png 712w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/poster_crop-300x300.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/poster_crop-150x150.png 150w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c8d7448 elementor-widget elementor-widget-image\" data-id=\"c8d7448\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"688\" height=\"688\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/high_per_4_crop.png\" class=\"attachment-large size-large wp-image-252\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/high_per_4_crop.png 712w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/high_per_4_crop-300x300.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/high_per_4_crop-150x150.png 150w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-47c2890 elementor-widget elementor-widget-image\" data-id=\"47c2890\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"688\" height=\"688\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/board.png\" class=\"attachment-large size-large wp-image-313\" alt=\"\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/board.png 712w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/board-300x300.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-content\/uploads\/sites\/69\/2025\/01\/board-150x150.png 150w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Research Dissertations MRes. In statistics and operational research (Lancaster University, 2025) Supervisors: Israel Mart\u00ednez-Hern\u00e1ndez (Lancaster University), Emma Eastoe (Lancaster University),&hellip;<\/p>\n","protected":false},"author":91,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-2","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/users\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":82,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":635,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/pages\/2\/revisions\/635"}],"wp:attachment":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/roberto-vasquez-martinez\/wp-json\/wp\/v2\/media?parent=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}