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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Asymmetric GARCH modelling without moment conditions
[Submitted on 1 Oct 2024 (v1), last revised 30 Jun 2026 (this ve · 2024-10-01 · via stat updates on arXiv.org

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Abstract:Heavy tails and stability are two persistent challenges in modelling financial time series, yet most existing approaches rely on finite-moment assumptions and pay insufficient attention to stability issues. To bridge this gap, we propose an asymmetric GARCH model with standardized non-Gaussian stable innovations (sAGARCH), which accommodates infinite variance and even infinite mean. We establish a comprehensive inference framework for both stationary and explosive cases, proving the strong consistency and asymptotic normality of the maximum likelihood estimator, including the tail index parameter. We also discuss multiple estimators for the asymptotic variance. Additionally, we propose a modified Kolmogorov-type test statistic for diagnostic checking, along with tests for strict stationarity and asymmetry. Through Monte Carlo simulations with heavy-tailed innovations, we provide further insight into the finite-sample performance of the intercept estimator. Empirical applications to stock returns further highlight the usefulness and merits of the proposed sAGARCH model.

Submission history

From: Yuxin Tao [view email]
[v1] Tue, 1 Oct 2024 10:43:26 UTC (1,811 KB)
[v2] Tue, 30 Jun 2026 06:08:40 UTC (278 KB)