Understanding Rare Events and Anomalies: Why streaks patterns change
We often look back at the past year and an overall history of rare events, and try to then extrapolate future odds of the same rare event, based on that. We illustrate here, that rare past events have no usefulness in understanding the rarity of the same events in the future!
So over each of the 6 time periods identified, we measure the record number of days in each of the following 7 broad market patterns we analyze below (green is an up-day in the market and red is a down-day). What is shown is merely illustrative:
To read the results below, we can take the example of an “alternating”. In 1950 the lengthiest streak of this pattern was 5 days.  The following year the lengthiest streak was 4 days (the new 4-day pattern is less rare). However in 1952-1953, the lengthiest streak surged to 8 days (a rarer streak was established versus the cumulative record of 5 days from the prior 2-year period of 1950-1951).
The results basically affirm that rarer records (shown in red) are the norm across all 7 events (which itself is highly significant to consider streaks run in all directions!)  However, there has been a recent reversal where the market has seen smaller (less rare shown in green) streaks across all 7 events, despite all of the arguments about the effect of quantitative easing (here, here). One should balance this with their own intuition. While this reversal is significant, we can’t state with the sample -for this correct analysis- whether it is simply more random or if we can expect a trend in less rare events to go forward.  Also notice that only scarcely does the streak pattern in the past stay the same (yellow color)… So much for pattern mining!
Only if the latter is true, we should see streak patterns arbitraged away. Nassim Taleb’s ideas would therefore be flawed relative to Eugene Fama’s efficient-market hypothesis, and we would expect that we see immensely random (regardless of any wild gyrations) markets for many years going forward. And flattish markets in 2015 would tell us absolutely nothing about 2016.
And with that, happy holidays! Looking forward to catching up in the new year. Off topic: If you, or someone you know, would enjoy writing a policy AND statistics article, for a diverse and prestigious, academic peer-reviewed American Statistical Association journal, then please reach out to me as soon as possible, at this e-mail address below. I (as an associate editor) can help facilitate. Thanks! salil.mehta@georgetown.edu
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