# Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes

arXiv: https://arxiv.org/abs/1502.06557 · HTML: https://mlsanity.com/paper/1502.06557/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2015.

## Built on by (most cited first, 7 of 7)

- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Heteroscedasticity-aware residuals-based contextual stochastic optimization](https://mlsanity.com/paper/2101.03139/) (2021)
- [Smoothed Bernstein Online Aggregation for Day-Ahead Electricity Demand Forecasting](https://mlsanity.com/paper/2107.06268/) (2021)
- [Online Distributional Regression](https://mlsanity.com/paper/2407.08750/) (2024)
- [Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression](https://mlsanity.com/paper/2309.08783/) (2023)
- [ℓ1-Regularized Generalized Least Squares](https://mlsanity.com/paper/2405.10719/) (2024)

## Abstract (arXiv)

Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR-ARCH type models efficiently. Extensions to the model like periodic AR-ARCH, threshold AR-ARCH or ARMA-GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.