I recently wrote a time series modeling algorithm. I tried some existing open-sources packages but none worked very well. I really just wanted to decompose the time-series into a set of linear trends merged together in a continuous way. It turned out there was an elegant algorithm to do this called L1TF from Boyd's convex optimization group at Stanford. Also found a python implementation on Github to get started with. The paper mentioned that it was easy to add all kinds of things such as seasonality, discontinuities, outlier rejection, auto-regression etc but didn't give formulas. Just waved the hand like many academic papers do. I ended up figuring out how to add all these things but in order to do so, I had to learn a large part of the field of convex optimization in my after-work and vacation time and perform some lengthy, difficult calculus to arrive at the formulas. The algorithm worked great in the end. I find it funny that while the client is satisfied, they no idea that they now possess one of the world most powerful time-series algorithms which involves ideas from some of history's greatest mathematicians: Newton, Lagrange, Euler, von Neumann as well as many of the past century's luminaries. Open source part is here. https://github.com/dave31415/myl1tf