  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.
