📈Econometrics & Finance

Abstract

The generative-AI boom of 2021–2025 drove technology stocks to unprecedented highs and raised pressing questions about how extreme downside risk in these high-growth names stacks up against traditional large-value equities. In this thesis, we quantify and compare the one-day 99% Value-at-Risk (VaR) of an equally weighted portfolio of ten AI-growth stocks versus ten large-value stocks, using both nonparametric Historical Simulation (HS) and symmetric GARCH(1,1) models with Gaussian and Student-t innovations. We then subject each VaR estimate to regulatory-style back-tests: Kupiec’s Unconditional Coverage and Christoffersen’s Conditional Coverage, to assess their adequacy for capital calculation. Empirically, the AI portfolio exhibits a mean one-day 99% VaR of 4.997%, more than double the 2.084% observed for the Value portfolio. Violation rates under HS, Student-t GARCH, and Gaussian GARCH are 1.49%, 1.60%, and 1.95% for AI versus 1.03%, 1.26%, and 1.38% for Value. Only HS and Student-t GARCH pass all back-tests. These findings underscore the critical importance of fat-tailed or nonparametric methods when measuring risk for high-growth equity portfolios, with direct implications for setting regulatory capital.

Abstract

In this blog post, I rigorously analyze the forecasting performance of commodity price inflation models. I compare a conventional univariate autoregressive (AR) model with two mixed frequency models—the unrestricted MiDAS model and the HAR-MiDAS model. By integrating daily stock returns with monthly inflation data, I aim to capture market dynamics that standard techniques overlook. I evaluate model performance using robust statistical tests, RMSE comparisons, and the Diebold-Mariano test, and I explore the benefits of a rolling forecast origin. Throughout the analysis, I include detailed mathematical formulations, estimation results, tables, and graphical visualizations.

Introduction

Bootstrapping is a resampling method that enables the estimation of the sampling distribution of a statistic by drawing repeated samples with replacement from the observed data. In simple terms, imagine you have a jar filled with cookies. Instead of baking a new jar of cookies to see how the average size might vary, you repeatedly pick a handful of cookies from the same jar (with replacement), calculate the average size for each handful, and then study how these averages vary. This variation gives you an insight into the reliability and variability of your original measurement.

Abstract

This blog post presents an innovative and comprehensive analysis of Portugal’s macroeconomic performance over the period 1970–2005. By integrating classical economic theory with advanced econometric modeling—including Vector Autoregression (VAR) and ARIMA approaches—we examine the intricate interplay between GDP growth, unemployment, and inflation. Our study revisits the traditional Phillips Curve framework and proposes an accelerated variant to better capture the nuances of Portuguese economic dynamics. The analysis not only identifies key recession periods but also offers robust policy implications for economic stabilization and investment strategy formulation.