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.

About Ito's Process

Besides Black & Scholes, Kiyoshi Ito is one of the really popular guys in mathematical finance. Everybody in the scene knows his diffusion process, and I have some problems with it!

Ito's Diffusion Process (Simplest form):

Given that X(t) is a random variable, representing price of a financial security at time t, the change in X can be represented by,

dX(t)= aX(t)dt + sdW(t)

where

a, s: constants with respect to the model applied
W(t): Brownian motion


Stylized Facts
Empirical findings have however shown that the markets are NOT truly random as suggested by the Brownian motion. D. Whitcomb has pointed out a negative serial correlation off Index returns since 1979! Here's an article about his findings. This means the drift parameter a above does not always make sense. Yeah, there's always the drift due to inflation on indexes, but not all securities can even keep up with it, especially those with high credit risk.

The conditional variance contradicts with a lot of existing academic assumptions around Heston's stochastic volatility paper. Well it isn't so stochastic if you've actually observed volatility time series critically. I can't get into the volatility thing until a later time.

That's it for now!