New methods for multivariate distribution forecasting

This thesis contributes to the current literature in finance and economics by introducing new methods for forecasting and accuracy evaluation. First, we propose and develop a new multivariate distribution forecasting method. Second, we compare proper scoring rules through a discrimination measure. Our Factor Quantile models are exible semi-parametric models for multivariate distribution forecasting where conditional marginals have a common factor structure, their distributions are interpolated from conditional quantiles and the dependence structure is derived from a conditional copula. A version based on latent factors can be constructed using endogenous principal component analysis. We present a comprehensive comparison of Factor Quantile models with GARCH and copula models for forecasting different multi- variate distributions which is the first extensive application of proper multivariate scoring rules for financial asset returns. Our empirical study employs daily USD exchange rates from 1999 - 2018; US interest rates from 1994 - 2018; and Bloomberg investable commodity indices from 1991 - 2018 with eight time series in each system, yielding almost 1 million predictions. Formal testing indicates favourable forecasting performance of Factor Quantile models, matching or exceeding the accuracy of more complicated GARCH models, which take at least six times longer to calibrate and may also exhibit difficulties with parameter optimisation even when the multivariate distribution has only few dimensions. In a simulation study, we analyse the ability of multivariate proper scoring rules to determine the true data generating model. We apply a new discrimination measure to the energy score and different parameterizations of the variogram score. Then, we evaluate the performance of this metric in standard tests of superior predictive ability. Previous literature generally agrees that the ideal score depends on the data and models. However, our findings clearly identify the variogram score with p = 1 as the most successful score in all three data sets, largely irrespective of the choice for the data generating model.