Testing for change in mean of heteroskedastic time series

TL;DR

This paper introduces a Lagrange Multiplier test for detecting mean changes in heteroskedastic time series, demonstrating its theoretical properties, simulation performance, and practical application to stock index data.

Contribution

It develops a new LM test for mean change detection in heteroskedastic time series, with proven consistency and applicability to real-world financial data.

Findings

The test maintains good size and power in moderate samples.

It effectively detects both abrupt and smooth mean changes.

Application to S&P 500 data illustrates practical usefulness.

Abstract

In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perform also some Monte Carlo simulations to analyze the size distortion and the power of the proposed test. We conclude that for moderate sample size, the test has a good performance. We finally carry out an empirical application using the daily closing level of the S&P 500 stock index, in order to illustrate the usefulness of the proposed test.