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Activity Number: 89 - Nonparametric Methods for Modern Data
Type: Contributed
Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
Sponsor: Section on Nonparametric Statistics
Abstract #318840
Title: Wasserstein Autoregressive Models for Density Time Series
Author(s): Chao Zhang* and Piotr Kokoszka and Alexander Petersen
Companies: University of California, Santa Barbara and Colorado State University and Department of Statistics and Applied Probability, UC Santa Barbara
Keywords: Random Densities; Wasserstein Metric; Time Series; Distributional Forecasting
Abstract:

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


Authors who are presenting talks have a * after their name.

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