Change-Point Models: What Are They and Why Do We Need Them?

Introduction

So what is a "change point"? Formally, a change point is a point at which the statistical properties of a model change. But what does that actually mean? Suppose that we are trying to fit a linear model to the data shown in Figure 1a, which was generated by a piecewise function with added white noise. More specifically, the points were determined by the equations

Y(1:14) = 4+N(0, 0.04),
Y(15:30) = 6+N(0, 0.04),

where N(0, 0.04) denotes a random sample from a normal distribution with mean 0 and variance 0.04, ie., random variability around the mean.