# Yule's disturbed pendulum time series example

In his 1927 paper On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers, Udny Yule considers a thought experiment where there is a simple pendulum hanging from a fixed point and whose natural path is disturbed by pea shots from children; the example motivates the first use of the autoregressive model for time series analysis.

Is there a data set (with real data) available that will illustrate this pendulum example?

Since you are looking for only a pendulum, and not a generic time series with random noise (like @blairchristian posted), then I would consider simulating the data.

Here is an example of a pendulum code, although you don't need the visualization part. It's a pretty common coding assignment (not as common as double pendulum it seems), so you can probably find your favorite code.

To add the random perturbations, you just need to determine which dimensions are allowed (i.e. if the pendulum is like the Foucault Pendulum, the perhaps the peas can only add random force in the horizontal plane of motion.)

just for fun, consider using quasi-random perturbations that have burst or breakout behavior, like

• stock market volume deviation from the mean of that day of the week (example, Apple stock over last 10 years)

• live data, i.e. from the twitter public stream, that perturbs the pendulum based on the occurrence of tweets or aggregate data from tweets

• Those are interesting ideas on how to generate perturbations. But, of course, it isn't hard to generate the data I'm asking for. I was hoping for actual measurements from an actual experiment. Jan 28, 2015 at 20:23
• It was a though experiment in 1927. Maybe no one has done the exact measurement, let alone shared the data.
– philshem
Jan 28, 2015 at 20:55
• That may be the case. I certainly wasn't successful finding the data anywhere. This site seemed to be the place to ask, though. Jan 31, 2015 at 16:41

This paper, "Sunspot cycle simulation using random noise", might be a good place to start:

http://tf.boulder.nist.gov/general/pdf/230.pdf

Actual sunspot data here:

http://www.swpc.noaa.gov/products/solar-cycle-progression

• Unfortunately, it seems I haven't been very clear. I am seeking data that illustrates the disturbed pendulum. Jan 2, 2015 at 23:22