# Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series

arXiv: https://arxiv.org/abs/2304.03069 · HTML: https://mlsanity.com/paper/2304.03069/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 4 of 4)

- [Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?](https://mlsanity.com/paper/1511.03688/) (2015)
- [Exploiting statistical dependencies of time series with hierarchical correlation reconstruction](https://mlsanity.com/paper/1807.04119/) (2018)
- [Adaptive exponential power distribution with moving estimator for nonstationary time series](https://mlsanity.com/paper/2003.02149/) (2020)
- [Parametric context adaptive Laplace distribution for multimedia compression](https://mlsanity.com/paper/1906.03238/) (2019)

## Built on by (most cited first, 2 of 2)

- [Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals](https://mlsanity.com/paper/2305.09478/) (2023)
- [Adaptive stable distribution and Hurst exponent by method of moments moving estimator for nonstationary time series](https://mlsanity.com/paper/2506.05354/) (2025)

## Abstract (arXiv)

The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time t finding parameters optimizing e.g. Ft=sumτ<t (1-η)t-τ ln(ρθ (xτ)) moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments mp=E[|x-μ|p] evolving for one or multiple powers p∈ℝ^+ using mp,t+1 = mp,t + η (|xt-μt|p-mp,t). Application of such general adaptive methods of moments will be presented on Student's t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of μ and σ, here we also get evolution of nu describing ρ(x)~ |x|-nu-1 tail shape, probability of extreme events - which might turn out catastrophic, destabilizing the market.