# Nonparametric volatility change detection

## TL;DR

This paper introduces nonparametric tests for detecting changes in the conditional variance of heteroscedastic time series, combining empirical process methods with classical CUSUM tests, and demonstrates their effectiveness through simulations and real data.

## Contribution

It proposes new nonparametric change detection tests for variance functions that are consistent and asymptotically distribution-free in certain cases.

## Key findings

- Tests are consistent against general alternatives.
- Asymptotically distribution-free for univariate covariates.
- Good performance demonstrated in simulations and exchange rate data.

## Abstract

We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests with marked empirical process approaches known from goodness-of-fit testing. The tests are consistent against general alternatives of a change in the conditional variance function, a feature that classical CUSUM tests are lacking. We derive a simple limiting distribution and in the case of univariate covariates even obtain asymptotically distribution-free tests. We demonstrate the good performance of the tests in a simulation study and consider exchange rate data as a real data application.