By Hudson Cooper
In the left panel, we plot the yearly maximum United States unemployment rate since 1948, updated on a quarterly basis.
The right panel shows the unconditional probability of exceeding a given unemployment rate over the course of a year. The points marked “Observations” are the empirical probabilities of these excesses and are given by Weibull plotting positions.
On a yearly basis, a Generalized Extreme Value (GEV) distribution is fit to the observations, and its predicted probabilities are represented with a solid curve. A confidence band reflecting model uncertainty due to variability in the data is represented as a blue shaded region.
The GEV distribution is an important model because it not only allows us to extrapolate the historical frequency of extreme events to “unprecedented” future events, it also allows us to realistically capture our (asymmetric!) uncertainty of these estimates.
The animation shows how the GEV models and their uncertainties change as they are given access to more historical data. We see that as more extreme events (unusually high unemployment rates) occur, the model updates its beliefs accordingly, attributing higher probabilities to these events and slightly reducing the uncertainty in this region.
While historical empirical probabilities are prone to underestimating the future empirical probability of extreme events, the GEV model describes these occurrences more faithfully. When the GEV model fails, it also tends to underestimate these probabilities, but these failures are well-represented by the asymmetric confidence bands.
Source: U.S. Bureau of Labor Statistics, Unemployment Rate [UNRATE], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/UNRATE