The Pitfalls of Continuous Heavy-Tailed Distributions in High-Frequency Data Analysis

Battle Count: 79

Highly relevant for quantitative trading practitioners working with high-frequency data. The paper provides critical warnings about common modeling pitfalls (using standard GARCH with continuous distributions on discrete tick data) that could lead to misleading volatility estimates. The proposed interval MLE framework is directly applicable to intraday volatility estimation, which is essential for execution algorithms, market making, and short-term risk management. The finding that Student's t works at 1-minute but not 1-second frequencies provides practical guidance for model selection. However, the paper is more diagnostic/methodological than directly producing trading signals.

The core idea (replacing density evaluation with interval probability) is conceptually simple and requires only modifying the log-likelihood function. However, practical implementation involves: (1) computing CDF differences for the Student's t-distribution, (2) deriving the modified score function for the GAS model, (3) estimating diurnal patterns via smoothing splines, (4) handling numerical issues with extreme parameter values, and (5) proper data cleaning and aggregation. The author provides R code via GitHub, reducing implementation burden. The gasmodel package is needed for the proposed approach.

Data available on GitHub (github.com/vladimirholy/continuous-high-frequency-garch). R packages specified (rugarch, fGarch, GAS, gasmodel). Standard data cleaning steps from Barndorff-Nielsen et al. (2009) described. However, the interval MLE implementation details and smoothing spline specifications for diurnal patterns could benefit from more explicit code documentation. The gasmodel package by the same author is referenced but may not be widely available.