What's the probability of a future polling result falling in a given range?

Question

Question

Each day, Gallup polls U.S. Employee Engagement. You can see 7-day rolling averages of the daily numbers here.

Assume you have a set of historical daily numbers (ie, [0.354827, 0.352648, 0.34943, …]). What would be the best technique to estimate the probability of a future number falling in a given range?

As an example, I may want to say "the probability of the number three days from now falling in the range 0.45…1 is ____%."

Initial Attempt

My initial attempt counted the # of times this range condition had been met in the last 90 days, but this has a number of flaws. Most notably, the ranges 0…0.01 and 0…0.15 were equally unlikely, but obviously the former should be less likely than the latter.

That is, my initial attempt didn't consider that the results tend to hover around 0.30…0.33.

Related Questions

I read Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency. The question seemed related, but not identical, and the answer was over my head. I started reading about ARIMA models, but I didn't want to get too far into the weeds without knowing if that's the right approach here.

Answer 1

This is related to what is known as a Credible Interval which is similar but distinct from a confidence interval. Credibility intervals are constructed using a probability of correctness expressed as a percentage. This is the percent chance that the true value falls within the interval. What you wish to do is reverse engineer a credibility interval: go from an interval to a percentage.