Figure 8

Analytical comparison of U.S. economic recession. We modeled the log odds ratio of a U.S. economic recession using three ordinary least squares regression models. Each model used one of the ADV method’s anomaly indicator, the shock indicator function resulting from the discrete shocklet transform, and the windows of shock-like behavior output by the STAR algorithm as elements of the design matrix. The models that used features constructed by the DST or STAR outperformed the model that used features constructed by ADV as measured by both \(R^{2}\) (displayed in the top panel) and model log-likelihood. The black curve in the top panel displays the null distribution of \(R^{2}\) under the assumption that no regressor (column of the design matrix) actually belongs to the true linear model of the data [91, 92]. The lower panel displays the empirical probability distributions of the model residuals \(\varepsilon _{i}\)