I recently had to fix my backyard fence. It is old, wooden and has been threatening to fall for a long time. Between curses, it really surprised me how many tools I needed to use to get the job done and how sometimes you really need more than one tool for the job.
What does this have to do with time series regression? In general, very little. In particular, quite a bit: Today we will dive into the use of mixture models for time series analysis and forecasting. Or in more terms: use more modeling tools to do the forecasting work.
So, without rambling much further, we'll start with:
- Reviewing the big picture and talking a little about mixed models.
- Looking at some real world data.
- Using a simple model to capture the trend in our time series.
- Seasonality in three forms: decision trees, linear regression and classical time series.
- Reassemble Humpty Dumpty to get a single time series prediction.
Aside: You'll be happy to know that my thumbs have fully recovered after a few hammer-related accidents.
As always, we are trying to build the most “accurate” model possible. In this case, we focus on forecasting, so we will prioritize models that can produce the most accurate estimates of future values of the time series.
I previously wrote extensively about using a regression approach based on the Meta's Prophet methodology. In those articles, I explained why I chose to use the LASSO model: non-stationarity made it difficult to use classical methods, the need for sensible extrapolation ruled out tree-based approaches, and the desire for simplicity and explainability excluded any type of neural network. .
But I also hinted at using mixed model forms, that is, modeling each of the components of the time series using a different model form and combining the output of…
