The resonance of a single-degree-of-freedom forced nonlinear system with two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms and the excitation force with close frequencies is examined. The method of multiple scales is...

We propose a “reflexivity” index that quantifies the relative importance of short-term endogeneity for several commodity futures markets (corn, oil, soybean, sugar, and wheat) and a benchmark equity futures market (E-mini S&P 500), from mid-2000s to October 2012. Our reflexivity index is...