Sunday, November 7, 2010

About spurious correlations

I was talking to a fellow mathematician, someone not familiar with financial economics, around autocorrelation within financial data. "It could be spurious..." he said, implying and concluding that the relationship may not be practically exploitable.

OK, so the next logical thought is, even if the correlation IS spurious, can it still be applied somehow?

(Above figure gives HFRI Hedge Fund Index Autocorrelations for the indicated period)

Spuriousness explained

William C. Burns has given a great example of a spurious correlation,

  1. Get data on all the fires in San Francisco for the last ten years.
  2. Correlate the number of fire engines at each fire and the damages in dollars at each fire.
Note the significant relationship between number of fire engines and the amount of damage. Conclude that fire engines cause the damage.

So basically, it means that correlation statistics do not explain cause and effect orders.

Some relationships remain exploitable

OK, so let's go back to significant correlations of stock index values against Dividend Yield or the autocorrelation thing. Fundamentally speaking these relationships may make sense with respect to expected rational behavior of institutional traders. However, someone who does not have a background in financial economics would assume spuriousness.

Does it really matter? Referring to serial correlation, so what if a security's return at time t, S(t) depends on S(t-1), or that maybe S(t-1) depends on S(t); as long as the relationship's there and statistically significant, it is probably exploitable. The bottom line is everything.

0 Reflections: