Research
Dissertations
MRes. In statistics and operational research (Lancaster University, 2025)
Supervisors: Israel Martínez-Hernández (Lancaster University), Emma Eastoe (Lancaster University), Wagner Barreto-Souza (University College Dublin)
Description: 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.
MSc. in Probability and Statistics: Partial Least Squares for non-stationary time series: A forecasting Approach (CIMAT, 2024)
Supervisors: Graciela González-Farías (CIMAT), Israel Martínez-Hernández (Lancaster University)
Description: 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.
Publications
- 2025 Vasquez Martinez, R, Gonzalez Farias, G, Marquez Urbina, J U & Corona, F. Over the Stability of a
Non-Stationary Multivariate Time Series. doi:10.48550/arXiv.2506.22407. - 2023 Gonzalez Farias, G, Vasquez Martinez, R, Marquez Urbina, J U& Ramos Quiroga, R. A Gompertz
Mixture Approach for Modeling the Evolution of the COVID-19 Dynamics. Revista de Matemática: Teoría y Aplicaciones. doi:10.15517/rmta.v30i1.50927. - 2022 Vasquez Martinez, R, Villarreal Haro, K, Sanchez Leon, C A, Ortiz Arana, E I, Cardenas Treviño, J
A& Martin, Gonzalez, E M. Conditional Passing Times for Cramer-Lundberg Risk Model. Jovenes en la
Ciencia 16. Link
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