Wasserstein autoregressive models for density time series

Data consisting of time-indexed distributions cross-sectional or intraday returns have been extensively studied in finance, and provide one example which the data atoms consist serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series exploiting tangent space structure on that is induced Wasserstein metric. The densities themselves are not assumed to any specific parametric form, leading flexible forecasting future unobserved densities. main estimation targets order-p autocorrelations vector-valued parameter. We suitable estimators establish their asymptotic normality, verified a simulation study. new leads prediction algorithm, includes driven order selection procedure. Its performance compared existing procedures via application four financial return sets, where variety metrics used quantify accuracy. For most metrics, proposed outperforms methods two while best empirical other sets attained based functional transformations