In timeseries data, usually it can decomposed into trend, seasonality, and influence from other control variables. In GLM, we can model a timeseries by de-trend regression data. However, there is a problem with prediction, as if we predicted for enough into the future, (linear) trend could grow without bounds

For timeseries forecast model like Holt’s model, it added dampening terms such that trend would decayed to a constant value at some point. But if I use GLM, I don’t have the same formulation as it is not autoregressive

I have the idea of using exponential decay to mimic this behaviour, but it became a hyper-parameter that is not optimized in the model. I’ve made a draft formulation using desmos here. Now, I want to reformulate this such that it is learnt with the graphical model, any ideas?