A signed power transformation with application to white noise testing

TL;DR

This paper introduces a signed power transformation that preserves ARCH-type properties in processes, aiding in white noise testing especially when fourth moments are undefined and for detecting non-ARCH white noise.

Contribution

It presents a novel signed power transformation that maintains ARCH-type structure, expanding tools for white noise testing in complex stochastic processes.

Findings

Signed power transforms of ARCH processes remain ARCH-type.

Applicable to models lacking fourth moments.

Useful for detecting non-ARCH white noise.

Abstract

We show that signed power transforms of some ARCH-type processes give ARCH-type processes. The class of ARCH-type models for which this property holds contains many common ARCH and GARCH models. The results can be useful in testing for white noise when fourth moments don't exist and detecting white noise that is not ARCH-type.