# Parsimonious Quantile Regression of Financial Asset Tail Dynamics via Sequential Learning

arXiv: https://arxiv.org/abs/2010.08263 · HTML: https://mlsanity.com/paper/2010.08263/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Likelihood Annealing: Fast Calibrated Uncertainty for Regression](https://mlsanity.com/paper/2302.11012/) (2023)
- [Regularization Strategies for Quantile Regression](https://mlsanity.com/paper/2102.05135/) (2021)
- [Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control](https://mlsanity.com/paper/2602.02592/) (2026)
- [DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting](https://mlsanity.com/paper/2508.02616/) (2025)

## Abstract (arXiv)

We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time series. It combines the merits of a popular sequential neural network model, i.e., LSTM, with a novel parametric quantile function that we construct to represent the conditional distribution of asset returns. Our model also captures individually the serial dependences of higher moments, rather than just the volatility. Across a wide range of asset classes, the out-of-sample forecasts of conditional quantiles or VaR of our model outperform the GARCH family. Further, the proposed approach does not suffer from the issue of quantile crossing, nor does it expose to the ill-posedness comparing to the parametric probability density function approach.