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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:"

$$\gamma_j = \left(s_j - m - \sum_{l<j}\gamma_l \right)\left(1 - \frac{k + \sum_{l<j} \delta_l}{k + \sum_{l \leq j} \delta_l} \right)$$

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?

Link to paper: https://peerj.com/preprints/3190/

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Asked a friend, for anyone interested here how to come up with adjustment factor

Computing adjustment factor

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