In the paper it emphasizes:

"When the rate k is adjusted, the offset parameter m must also be adjusted to connect the endpoints of the segments. The correct adjustment at changepoint j is easily computed as:"

$$\gamma_j = \left(s_j - m - \sum_{l

My understanding is, adjustment makes sure function is still continuous.

I have 2 questions regarding this model that are not explained in the paper:

How do we come up with the result function is not continuous without the adjustment factor, and how do we compute the adjustment factor?