  A change point problem occurs in many statistical applications. If there
exist change points in a model, it is harmful to make a statistical analysis
without any consideration of the existence of the change points and the results
derived from such an analysis may be misleading. There are rich literatures on
change point detection. Although many methods have been proposed for detecting
multiple change points, using these methods to find multiple change points in a
large sample seems not feasible. In this article, a connection between multiple
change point detection and variable selection through a proper segmentation of
data sequence is established, and a novel approach is proposed to tackle
multiple change point detection problem via the following two key steps: (1)
apply the recent advances in consistent variable selection methods such as
SCAD, adaptive LASSO and MCP to detect change points; (2) employ a refine
procedure to improve the accuracy of change point estimation. Five algorithms
are hence proposed, which can detect change points with much less time and more
accuracy compared to those in literature. In addition, an optimal segmentation
algorithm based on residual sum of squares is given. Our simulation study shows
that the proposed algorithms are computationally efficient with improved change
point estimation accuracy. The new approach is readily generalized to detect
multiple change points in other models such as generalized linear models and
nonparametric models.

Methodology