  A new approach to detect change points based on differential smoothing and
multiple testing is presented for long data sequences modeled as piecewise
constant functions plus stationary ergodic Gaussian noise. As an application of
the STEM algorithm for peak detection developed in
\citet{schwartzman2011multiple} and \citet{cheng2017multiple}, the method
detects change points as significant local maxima and minima after smoothing
and differentiating the observed sequence. The algorithm, combined with the
Benjamini-Hochberg procedure for thresholding p-values, provides asymptotic
strong control of the False Discovery Rate (FDR) and power consistency, as the
length of the sequence and the size of the jumps get large. Simulations show
that FDR levels are maintained in non-asymptotic conditions and guide the
choice of smoothing bandwidth. The methods are illustrated in magnetometer
sensor data and genomic array-CGH data. An R package named "dSTEM" is available
in R cran.
