# MV Polar Bears Attendence Data Exploration and Forecasting

For the past several years, the wonderful MV Polar Bears group has recorded how many people attend each day. This post provides some basic visualizations of the dataset and an attempt to build a predicitive model to forecast the expected number of attendees. My big takeaways were:

- The MV Polar Bears are reaching an amazing number of people - wow!
- The bears are
*very*unpredictable.

## Attendence Over Time

The next plot shows the number of new and returning attendees over the past few years. There is a clear annual pattern, and always more old friends than new ones.

Polar bears are slowly creeping towards work domination! The plot below shows the cumulative number of attendees (blue) and new polar bear members (green) over time. The numbers are big and growing.

## What Drives Attendence?

Two features are related if knowing the value of one feature tells you something about the other. For example, the new and returning attendence number are closely correlated – when the group is bigger there are more “newbies”. Temperature and attendence show a different relation. Polar bears don’t sweat cold weather up to a point, and then attendence falls off a cliff. Take a look and see what else you can find.

## Forecast Model

Polar bears are hard to predict! You may notice from the plots above that attendence varies wildly from day-to-day, and the magnitude of this variation changes over time as well. These features make make building a predictor tricky. Moreover, I had hoped that the weather and water conditions might help to predict attendence, but it seems that Polar Bears aren’y much bothered by cold, wind, or rain.

After a bit of experimentation, I landed on a timeseries forecasting model that predicts changes in the mean and volitility (specifically a GARCH model with an ARX mean). The plot below shows retrospecitve predictions for the attendence dataset (top), as well as the prediction errors (bottom).

You may notice that the prediction is often *really* wrong. Like I
said, it is hard to predict polar bears! The volitility prediction works
better – the true number is usually within the (1-sigma) margin of
error.