The financial press has been buzzing about the results of an academic paper published by researchers from Indiana University-Bloomington and Derwent Capital, a hedge fund in the United Kingdom.

The model described in the paper is seriously faulted for a number of reasons:

**1. Picking the Right Data**

They chose a very short bear trending period, from February to the end of 2008. This results in a very small data set, “a time series of 64 days” as described in a buried footnote. You could have made almost 20% return over the same period by just shorting the “DIA” Dow Jones ETF, without any interesting prediction model!

There is also ambiguity about the holding period of trades. Does their model predict the Dow Jones on the subsequent trading day? In this case, 64 points seems too small a sample set for almost a year of training data. Or do they hold for a “random period of 20 days”, in which case their training data windows overlap and may mean double-counting. We can infer from the mean absolute errors reported in Table III that the holding period is a single trading day.

**2. Massaging the Data They Did Pick**

They exclude “exceptional” sub-periods from the sample, around the Thanksgiving holiday and the U.S. presidential election. This has no economic justification, since any predictive information from tweets should persist over these outlier periods.

**3. What is Accuracy, Really?**

The press claims the model is “87.6%” accurate, but this is only in predicting the direction of the stock index and not the magnitude. Trading correct directional signals that predict small magnitude moves can actually be a losing strategy due to transaction costs and the bid/ask spread.

They compare with “3.4%” likelihood by pure chance. This assumes there is no memory in the stock market, that market participants ignore the past when making decisions. This also contradicts their sliding window approach to formatting the training data, used throughout the paper.

The lowest mean absolute error in predictions is 1.83%, given their optimal combination of independent variables. The standard deviation of one day returns in the DIA ETF was 2.51% over the same period, which means their model is not all that much better than chance.

The authors also do not report any risk adjusted measure of return. Any informational advantage from a statistical model is worthless if the resulting trades are extremely volatile. The authors should have referenced the finance and microeconomics literature, and reported Sharpe or Sortino ratios.

**4. Backtests & Out-of-sample Testing**

Instead of conducting an out-of-sample backtest or simulation, the best practice when validating an un-traded model, they pick the perfect “test period because it was characterized by stabilization of DJIA values after considerable volatility in previous months and the absence of any unusual or significant socio-cultural events”.

**5. Index Values, Not Prices**

They use closing values of the Dow Jones Industrial Average, which are not tradable prices. You cannot necessarily buy or sell at these prices since this is a mathematical index, not a potential real trade. Tracking errors between a tradable security and the index will not necessarily cancel out because of market inefficiencies, transaction costs, or the bid/ask spread. This is especially the case during the 2008 bear trend. They should have used historic bid/ask prices of a Dow Jones tracking fund or ETF.

**6. Causes & Effects**

Granger Causality makes an assumption that the effects being observed are so-called covariance stationary. Covariance stationary processes have constant variance (jitter) and mean (average value) across time, which is almost precisely wrong for market prices. The authors do not indicate if they correct for this assumption through careful window or panel construction.

**7. Neural Parameters**

The authors do not present arguments for their particular choice of “predefined” training parameters. This is especially dangerous with such a short history of training data, and a modeling technique like neural networks, which is prone to high variance (over-fitting).

Making my way through your various blog posts. Great stuff! Had to laugh at this one. How did this paper ever get published? Obviously, these people have never traded. Anyway, great critique.