At a certain age, one gets used to being dumb. But it's still annoying to be dumb over and over again in the same way.

A few weeks back I posted on a very high correlation between the volume of index options, on the one hand, and the volume of the leveraged long and short index ETFs. I used a moving average to smooth out the data, and, of course, that was a mistake.

The two moving average series have a correlation of +0.959, but each also has autocorrelation in the +0.6 area. R has a nice function for checking autocorrelation, (acf), and here is a graph of the autocorrelation of one of the series. Lots of non-random structure in that graph.

To eliminate the autocorrelation problem, the volume data for the ETFs and for the index options was summed for each three days, and then the percent changes from one non-overlapping three-day period to the next were used to create two series of what should be independent data points. These series each showed about -0.2 autocorrelation at the 1-lag.

These two series have a correlation of +0.348. Which looks good, but then the next issue is: What if some underlying factor is causing the correlation?

The volume data for the NYSE was taken and converted into non-overlapping 3-day totals to match the index option and ETF series. Interestingly enough, this NYSE series also had a 1-lag autocorrelation of about -0.2.

More important, its correlation with the ETF series was +0.451, and with the index option series, +0.539. So both the ETF and index options volume series are more highly correlated with overall market volume than with each other.

Philip J. McDonnell writes:

The Slutsky-Yule Theorem is quite old and says that taking a moving average of a time series induces periodic motion even though none existed in the data itself. This topic arises periodically in this forum as well. One need not feel to bad after falling into this trap.

There is the famous story of Holbrook Working, a big name economist and arguably the best statistician in the government's employ. His paper, published in the 1960s compendium Random Character of Stock Market Prices seemed to show positive serial correlation in monthly prices. Thus it was a counterpoint to the argument for the random walk. The trend following crowd was born and looked to papers by Working, Alexander and Levy as proof that trend following was the Holy Grail.

Eventually the Working paper was debunked because he had used monthly average prices as his data set. This technique created the Slutzky-Yule effect and artificially induced the apparent serial correlation. When the defect was corrected the correlations were negative. The Alexander and Levy papers were also discredited but for different technical flaws.

Apparently some trend following hedge funds and best selling investment authors still have not received the word. 


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