The latest issue of Significance Magazine (a joint publication of the Royal Statistical Society, and the American Statistical Association), includes an interesting article by Ethan Brown and Nick Bearman. It's titled, "Listening to Uncertainty: Information That Sings".
The article is about "sonification" - listening to your data!
"Time series as a waveformA basic time series process that statisticians might have to study is an autoregression of the second order – which means that each piece of data depends on the piece before it and on thepiece two places before it as well. There may be random error in the data also. An equation for such a time series is
Xt = 0.6165Xt–1 – 0.995Xt–2 + εt
Xt is the value of the data at time t, Xt–1 is the value at the time just before it, and Xt–2 at the time two time-intervals before. εt is the error: it is normally-distributed white noise. We could graph this process but it just looks like a dense mat of points. The structure, however, becomes immediately apparent upon audification. We can listen to this data by picking a small unit of time (say, 0.1 milliseconds) and interpreting the time series as a sequence of sound pressure levels that a computer can play (sound available at soundcloud.com/tnt-yow/fuzz).
Yes, indeed, when we graph 5,000 values of this stationary time-series (with X1 and X2 both N[0, 1], and the variance of εt set to 1), this is what we see:When listening, it is immediately audible that there is a persistent pitched tone. Musical pitches are in fact periodic components of sound, so we are hearing that the time series has a periodic component. Part of it repeats over time. It would take complex techniques to show it visually; it is picked up straight away by the ear."
I listened to the same data on Soundcloud.com - very interesting. This series really does sound much better than it looks!
I also downloaded and played around with the Sonification Sandbox package that the authors mention on p.17 of their article. Lots of fun, and I can't wait to listen to some non-stationary series!
Perhaps we have new way of model validation in the making?
- Listen to your dependent variable and the potential covariates.
- Find a suitably harmonized sub-set of the covariates that's in the same key as your dependent variable.
- Listen to the predicted series. It should sound at least vaguely familiar!
- Listen to the residuals series. It should sound like your radio when you can't find a station within range.
I'm sure you get then basic idea!
© 2012, David E. Giles