Thursday, March 17, 2011

I can't hear you because it's too noisy

Odd title for a blog post, right? Well, it's my silly way to introduce a term which is often bantered about but not often discussed: "noise." No, I'm not talking about the sounds that come through the hotel room while you're trying to sleep or the sounds that interrupt your concentration. I'm speaking of "statistical noise."

In a recent post I introduced an animation that provides an overview of standard deviation. This post could have gone on and on and on, as this is a topic that has many angles on which to comment. And perhaps I'll do that in future posts, but for today we'll discuss noise and standard deviation.

What is noise?  Well, the often-criticized-but-frequently-cited Wikipedia defines it as "the colloquialism  for recognized amounts of unexplained variation in a sample." We anticipate that there will be some variance, but some of it comes from unknown sources, which makes it difficult to draw conclusions about what is occurring in our sample size or population.

Interestingly, we tend to get more noise as we shorten our time periods. For example, if we measure standard deviation over the past 36 months using daily returns, we're dealing with a great deal of noise. If, however, we lengthen our periods, our noise reduces. Thus, using months is quite common, though one might argue that quarters are better still, and why not move to years? Well, there are probably two reasons. One, for standard deviation to have much value we need at least 30 observations, and 30 quarters would equal 7 1/2 years, which may be too long as an organization can experience a lot of change over such a period. And 30 years would be even more difficult.

Yes, there's noise even in 36 months. And when (as the video pointed out) the distribution is probably not even normal, the value of the statistic is even more questionable / challengeable. No wonder it's a popular statistic both to use and discuss.

1 comment:

1. "Noise" usually implies that there exists a "signal". The noise/signal distinction is very big in engineering, information theory, science in general. I am not sure at all whether the signal/noise distinction makes sense in the context of security returns: price changes must follow a random walk on informatio efficient markets (random walks are noise processes). Even on only partially efficient markets, the price discovery process will result in "unexplainable" patterns (because the discovery process is a learning process about the unexplained). On the other hand, Modern Portfolio Theory is based on a signal / "noise" partition: systematic and unsystematic (=diversifiable noise) risk. Keynes wrote about signal/noise. "Noise" is a very interesting topic, but a "noisy" one :-)