Optimal Transport Autoregression to Forecast High‐Frequency Financial Data Distributions

ABSTRACT In this paper, we study the properties and performance of optimal transport autoregression in modeling and forecasting high‐frequency financial data distributions. We build on a class of univariate autoregressive transport models recently proposed in the literature (Zhu and Müller) where the distributional time series dynamics is modeled either through a single scalar, similarly with traditional Euclidean autoregressive models, or via a functional distribution‐contraction coefficient. Properties and performance of the models are investigated through an empirical application to forecast distributions of high‐frequency financial price returns and volatility of Bitcoin. Our results show that forecast errors are highly time‐ and quantile‐dependent: while autoregressive transport models are generally able to predict return and volatility densities during “normal business” periods, forecast errors tend to rise in the proximity of extreme quantiles, though such increase is non‐monotonic. We highlight the strengths and weaknesses of the method in modeling the distributional time series of high‐frequency, noisy financial data, suggesting some potential directions for future research.