Smoothing piecewise linear functions I have a piecewise linear function which is continuous.  I am looking for a good way to "smooth" the function at the boundary points.  Ideally, I would like a solution that's similar to A. Bellmunt's here:
A smooth function instead of a piecewise function
However, in my case, the slopes between each need not be $0$ or $1$, rather, they can be arbitrary.  Futher, I require that the "smoothed" section lie above each piece of my piecewise linear function.
What is the simplest such construction that exists?

If your output exhibits seasonality, you can use additional dummy variables to obtain a smoothed single linear function, something like this. This will get rid of piecewise linear functions and the discontinuity in derivatives therein.
