  We study the maximum score statistic to detect and estimate local signals in
the form of change-points in the level, slope, or other property of a sequence
of observations, and to segment the sequence when there appear to be multiple
changes. We find that when observations are serially dependent, the
change-points can lead to upwardly biased estimates of autocorrelations,
resulting in a sometimes serious loss of power. Examples involving temperature
variations, the level of atmospheric greenhouse gases, suicide rates, incidence
of COVID-19, and excess deaths during the pandemic illustrate the general
theory.
