Home on Juan Diego Mejía Becerra

Academic & Professional Background

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Academic Background

PhD in Statistics & Applied Probability | University of California, Santa Barbara (Expected 2026)

Dissertation: Perspectives on Statistical Limit Order Book Modeling
Committee: Gareth W. Peters (Co-chair); Ruimeng Hu (Co-chair); Michael Ludkovski
Concentration: Financial Mathematics & Statistics

MA in Statistics | University of California, Santa Barbara (2025)

Relevant Coursework: Advanced Financial Modeling, Stochastic Control, Functional Analysis, Statistical Machine Learning, Mathematical Statistics

MSc in Actuarial Science & Finance | Universidad Nacional de Colombia (2020)

Contact

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I am currently based in Goleta, California, and am open to discussing roles in Quantitative and Machine Learning Research.

Reach Out

Email: jmejiabecerra@ucsb.edu
Location: Goleta, CA

Professional Networks & Code

GitHub: github.com/judmejiabe
LinkedIn: linkedin.com/in/juan-diego-mejia-becerra

Publications

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On the Asymptotic Properties of the Conditional Maximum Likelihood Estimator for Time Series Regression Models with Conditional Heteroskedasticity

Juan Diego Mejía Becerra, Gareth W. Peters, Ruimeng Hu

In preparation

Overview: This paper addresses a significant gap in econometric theory by formally establishing the asymptotic properties of the Conditional Maximum Likelihood Estimator (CMLE) for ARMAX-GARCH models. While CMLE is widely employed in financial time series to model conditional heteroskedasticity with exogenous regressors, rigorous proofs of its efficiency have historically been limited. This research provides explicit, sufficient probabilistic conditions under which the CMLE is strongly consistent, asymptotically normal, and efficient—ultimately attaining the Fisher information bound. Key technical contributions include establishing geometric convergence rates for the recursive approximations of initial residuals and volatility seeds, alongside demonstrating the almost sure consistency of the outer product of score contributions.

Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting

Juan Diego Mejía Becerra, Gareth W. Peters, Ruimeng Hu

Working paper (Mar. 2026)

Overview: This paper bridges the gap between deep learning architectures and econometric inference in high-frequency trading by introducing the Two-Time-Scale Transfer Learning (TTSTL) framework. To overcome the non-stationarity and computational bottlenecks of pure neural networks, TTSTL couples a high-capacity CNN-LSTM “backbone”—which extracts complex, non-linear representations from event-driven Limit Order Book (LOB) data—with a lightweight ARMAX-GARCH “adapter” that rapidly recalibrates to local market dynamics. Regulated by an interface for dynamic feature selection via Flexible adaLASSO, this hybrid approach transforms deterministic neural network outputs into rigorous probabilistic forecasts. Validated on real-world Intel (INTC) Market-by-Order data, the TTSTL framework significantly outperforms standalone deep learning baselines in predictive accuracy.

What Benefits Drive Membership in Medicare Advantage Plans?

Ian Duncan, Juan Diego Mejía Becerra, Jiarui Yu

Springer (Jul. 2025)

Overview: This research investigates the primary drivers of membership and market penetration within Medicare Advantage (MA) health plans by analyzing a high-dimensional dataset of plan benefits, costs, and CMS quality metrics. To overcome the severe multicollinearity and overparameterization inherent in complex healthcare data, this study deploys Principal Components Regression (PCR) coupled with forward variable selection and rigorous residual diagnostics. By orthogonalizing the feature space through PCA before executing the regression, the model successfully isolates the precise statistical impact of specific plan features. The findings quantify the elasticity of market share with respect to financial constraints and reveal the outsized impact of non-financial drivers such as drug coverage, nutritional benefits, and star ratings.

A Proposed Condition-Based Risk Adjustment System for the Colombian Health Insurance Program

Ian Duncan, Juan Diego Mejía Becerra, Tamim Ahmed

North American Actuarial Journal (Aug. 2024)

Overview: This paper presents a structural overhaul of the Colombian Health Insurance Program’s (SGSSS) risk adjustment framework, addressing the severe financial and operational inefficiencies of its legacy age-sex-territory compensation model. By processing over 18 million person-years of exposure and mapping native diagnostic codes to 255 distinct clinical categories, this research engineers a unified, prospective, condition-based risk adjustment model. The proposed system replaces fragmented, retrospective legal compensations with a rigorous predictive framework calibrated to handle heavy-tailed claim distributions. Evaluated via tolerance curves, predictive ratios, and Area Under the Curve (AUC) metrics, the new model demonstrates superior accuracy in forecasting healthcare expenditures.

Research Interests

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Research Expertise

Econometrics & Computational Finance

Market Microstructure: High-frequency finance, limit order book reconstruction and simulation, and alpha signal detection.

Statistics and Machine Learning

Time Series Analysis: Theory, methods, and applications.

Risk Management & Actuarial Mathematics

Healthcare Risk Analytics: Risk adjustment and grouper condition models.
Epidemiological Modeling: Disease transmission modeling, scenario analysis, and resource forecasting.

Targeted Domains

Applied AI & Deployment

AI-Assisted Education: Applications of machine learning and large language models to enhance pedagogical frameworks and accelerate knowledge acquisition.

Statistics and Machine Learning

Kernel Methods: Theory, methods, and applications.

Econometrics & Computational Finance

Energy Economics: Energy grid load forecasting, volatility pricing, and infrastructure demands.
Environmental & Renewable Finance: Renewable asset optimization, carbon pricing dynamics, and climate-linked financial instruments.

Technical Infrastructure & Capabilities

Languages: Python, R, SQL.
Machine Learning & AI: PyTorch, scikit-learn, AI deployment.
Time Series & Econometrics: statsmodels, rugarch, glmnet, urca.
Data Engineering & Pipelines: NumPy, pandas, rpy2, Databento (high-frequency LOB data).
Infrastructure & Reproducibility: Git, Docker, Linux/Bash, Google Cloud Storage (GCS).