Analysis of Crisis Effects via Maximum Entropy Adjustment

Crises, such as the Covid‐19 epidemic, can affect economic time series by distorting historical trends and seasonal patterns with extreme values. The identification and adjustment of such extremes is important for the production of seasonally adjusted data; an ongoing challenge is the identification of a crisis' end, where the time series returns to more typical pre‐crisis dynamics. A secondary challenge is to model and analyze time series data with both missing values and extremes. This paper extends the maximum entropy framework to a generalized class of extreme values, including level shifts, temporary changes, and seasonal outliers. These outliers are described as a particular type of stochastic process that is latent, or unobserved, such that its removal increases the time series entropy. The proposed methods allow one to model and fit time series data using conventional tools in the presence of specified streams of extreme values, as well as missing values. Extreme value adjustment, with quantification of mean squared error, can then be obtained along with the seasonal adjustment; there is also a test statistic to directly compare two specifications of extremes. The techniques are illustrated in weekly employment data.