Uma abordagem generativa profunda para previsão de densidade de múltiplos passos

Abstract

In this dissertation, we introduce a deep generative model for multi-step density forecasting over univariate sequences of stock returns. It is based on a Bayesian recurrent neural network that operates under the premise that the conditional distribution of returns belongs to a family of skew Student's t-distributions. We also present measures of predictive accuracy based on Probability Integral Transformation and Maximum Mean Discrepancy (MMD) to separately evaluate the unconditional normality and the serial independence of the normal pseudo-residuals generated by univariate conditional distribution models. Using these measures, we then propose a Bayesian procedure to jointly compare the performance of two or more competing models over multiple univariate sequences. This procedure automatically controls the probability that one model will be declared more accurate than another because of luck, not because it has superior predictive ability. Experiments on real datasets show that introducing fat tails and skewness into the conditional density of our model we propose provides significant accuracy improvements. They also demonstrate that our model is better than mainstream alternatives in capturing the main distributional and dependency structure characteristics observed in sequences of returns.