  A method for change point detection is proposed. We consider a univariate
sequence of independent random variables with piecewise constant expectation
and variance, apart from which the distribution may vary periodically. We aim
to detect change points in both expectation and variance. For that, we propose
a statistical test for the null hypothesis of no change points and an algorithm
for change point detection. Both are based on a bivariate moving sum approach
that jointly evaluates the mean and the empirical variance. The joint
consideration helps improve inference as compared to separate univariate
approaches. We infer on the strength and the type of changes with confidence.
Nonparametric methodology supports the analysis of diverse data. Additionally,
a multi-scale approach addresses complex patterns in change points and effects.
We demonstrate the performance through theoretical results and simulation
studies. A companion R-package jcp (available on CRAN) is discussed.
