In an earlier post about forecasting, I mentioned the work by Nassim Taleb on the concept of black swan. In his remarkable book, “The Black Swan”, Taleb describes at length the characteristics of environments that can be subject to black swans (unforeseeable, high-impact events).
When we make a forecast, we usually explicitly or implicitly base it on an assumption of continuity in a statistical series. For example, a company building its sales forecast for next year considers past sales, estimates a trend based on these sales, makes some adjustments based on current circumstances and then generates a sales forecast. The hypothesis (or rather assumption, as it is rarely explicit) in this process is that each additional year is not fundamentally different from the previous years. In other words, the distribution of possible values for next year’s sales is Gaussian (or “normal”): the probability that sales are the same is very high; the probability of an extreme variation (doubling or dropping to zero) is very low. In fact, the higher the envisaged variation, the lower the probability that such variation will occur. As a result, it is reasonable to discard extreme values in the forecasts: no marketing director is working on an assumption of sales dropping to zero.