Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models

TL;DR

This paper introduces ScoPe, a finite sample, distribution-free method for constructing exact confidence regions for GARCH model parameters, improving inference accuracy without relying on moment assumptions.

Contribution

The paper proposes ScoPe, a novel permutation-based approach for finite sample inference in GARCH models, overcoming limitations of existing methods like SPS.

Findings

ScoPe provides exact coverage probabilities in finite samples.

ScoPe outperforms asymptotic and bootstrap methods in simulations.

Experiments on stock data validate ScoPe's effectiveness.

Abstract

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.