Beware the Precision
The masquerade problem: we tend to overestimate exponents of fractal processes because large deviations are rare and take time to appear, leading us to underestimate the severity of shocks.
THE IDEA
Beware the Precision
I have learned a few tricks from experience: whichever exponent I try to measure will be likely to be overestimated (recall that a higher exponent implies a smaller role for large deviations)—what you see is likely to be less Black Swannish than what you do not see. I call this the masquerade problem.
Let’s say I generate a process that has an exponent of 1.7. You do not see what is inside the engine, only the data coming out. If I ask you what the exponent is, odds are that you will compute something like 2.4. You would do so even if you had a million data points. The reason is that it takes a long time for some fractal processes to reveal their properties, and you underestimate the severity of the shock.
Sometimes a fractal can make you believe that it is Gaussian, particularly when the cutpoint starts at a high number. With fractal distributions, extreme deviations of that kind are rare enough to smoke you: you don’t recognize the distribution as fractal.
When to use it
Assessing risk in financial markets where rare crashes occur.
Modeling natural disasters like earthquakes or floods.
Evaluating tail risk in investment portfolios.
Analyzing network traffic or social media popularity distributions.
FROM THEORY TO EVERYDAY LIFE
In practice
Estimating exponent from data
Let’s say I generate a process that has an exponent of 1.7. You do not see what is inside the engine, only the data coming out. If I ask you what the exponent is, odds are that you will compute something like 2.4. You would do so even if you had a million data points. The reason is that it takes a long time for some fractal processes to reveal their properties, and you underestimate the severity of the shock.
Fractal masquerading as Gaussian
Sometimes a fractal can make you believe that it is Gaussian, particularly when the cutpoint starts at a high number. With fractal distributions, extreme deviations of that kind are rare enough to smoke you: you don’t recognize the distribution as fractal.
A MOMENT TO REFLECT
Put it to work.
Think of a real-world data series with extreme events. How might the precision of your estimated exponent be misleading?
In what contexts might you be underestimating the probability of rare events due to limited data?
How does the masquerade problem affect your confidence in statistical models?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)