General / Methodological

Hedging Forecast Combinations With an Application to the Random Forest ArXiv ID: 2308.15384 “View on arXiv” Authors: Unknown Abstract This papers proposes a generic, high-level methodology for generating forecast combinations that would deliver the optimal linearly combined forecast in terms of the mean-squared forecast error if one had access to two population quantities: the mean vector and the covariance matrix of the vector of individual forecast errors. We point out that this problem is identical to a mean-variance portfolio construction problem, in which portfolio weights correspond to forecast combination weights. We allow negative forecast weights and interpret such weights as hedging over and under estimation risks across estimators. This interpretation follows directly as an implication of the portfolio analogy. We demonstrate our method’s improved out-of-sample performance relative to standard methods in combining tree forecasts to form weighted random forests in 14 data sets. ...

Deep multi-step mixed algorithm for high dimensional non-linear PDEs and associated BSDEs ArXiv ID: 2308.14487 “View on arXiv” Authors: Unknown Abstract We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE). Our algorithm relies on the iterated time discretisation of the BSDE and approximates its solution and gradient using deep neural networks and automatic differentiation at each time step. The approximations are obtained by sequential minimisation of local quadratic loss functions at each time step through stochastic gradient descent. We provide an analysis of approximation error in the case of a network architecture with weight constraints requiring only low regularity conditions on the generator of the BSDE. The algorithm increases accuracy from its single step parent model and has reduced complexity when compared to similar models in the literature. ...