Testing for a constant coefficient of variation in nonparametric regression

TL;DR

This paper introduces a new statistical test for assessing whether the coefficient of variation remains constant in nonparametric regression models, with proven asymptotic properties and practical applications to financial time series.

Contribution

It proposes a novel test based on the L^2-distance between the squared regression and variance functions, including asymptotic analysis and bootstrap validation.

Findings

Test is asymptotically normal under null and alternative hypotheses.

Bootstrap method effectively evaluates finite sample properties.

Applicable to stationary processes with mixing conditions, useful for financial data.

Abstract

In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function and variance function. We prove asymptotic normality of a standardized estimate of this distance under the null hypothesis and fixed alternatives and the finite sample properties of a corresponding bootstrap test are investigated by means of a simulation study. The results are applicable to stationary processes with the common mixing conditions and are used to construct tests for ARCH assumptions in financial time series.