I was reviewing a presentation given as part of a short course in the machine learning genre today, and happened across the following two bullets, under the heading “Strictly Stationary Processes”:
- Predicting a time series is possible if and only if the dependence between values existing in the past is preserved also in the future.
- In other terms, though measures change, the stochastic rule underlying their realization does not. This aspect is formalized by the notion of stationarity
I began to grumble. Even though the rest of the talk is quite okay and useful, this kind of progression leaves bad impressions with students, suggesting that, somehow, non-stationary time series, let alone chaotic series, are impossible or at least very difficult to forecast. Some students go on to say nonsensical things about natural time series, or, at least, can be misled by demagogues who know these distinctions are not only abstract, they are subtle, and not widely understood.
This matter has been addressed most comprehensively and recently by Lenny Smith of the London School of Economics, both in an encyclopedia entry on “Predictability and Chaos”, and in an excellent little book I’m very fond of, Chaos: A Very Short Introduction.
Facts are, we’ve collectively come a long way since Lorenz, whether by using the methods sketched by Slingo and Palmer, or by Sugihara and Deyle based upon work by Takens, or by Ye, Beamish, Glaser, Grant, Hsieh, Richards, and Schnute. (Nice summary here.) Even the famous Lorenz butterfly is a the subject of ordinary exposition.
Stochastic-based search and optimization is a major industry these days. I make a good chunk of my professional living from it.
So I think presentations ought to be more careful in what they say.
Then again, maybe I’m just a grumbly old codger.