# Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches

## TL;DR

This paper compares two nonparametric methods for robust ARCH testing under misspecified conditional mean models, finding polynomial approximation regression generally outperforms kernel regression in simulations.

## Contribution

It introduces and evaluates two nonparametric approaches for ARCH testing that are robust to misspecification of the conditional mean.

## Key findings

- Polynomial approximation regression outperforms kernel regression in simulations.
- Both methods do not require specifying the conditional mean model.
- The approaches are adaptable to various nonlinear models.

## Abstract

This study compares statistical properties of ARCH tests that are robust to the presence of the misspecified conditional mean. The approaches employed in this study are based on two nonparametric regressions for the conditional mean. First is the ARCH test using Nadayara-Watson kernel regression. Second is the ARCH test using the polynomial approximation regression. The two approaches do not require specification of the conditional mean and can adapt to various nonlinear models, which are unknown a priori. Accordingly, they are robust to misspecified conditional mean models. Simulation results show that ARCH tests based on the polynomial approximation regression approach have better statistical properties than ARCH tests using Nadayara-Watson kernel regression approach for various nonlinear models.