A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasiconvex, nor...

This paper presents different deep neural network architectures designed to forecast the distribution of returns on a portfolio of U.S. Treasury securities. A long short-term memory model and a convolutional neural network are tested as the main building blocks of each architecture. The models...