Time-Series Imputation with Wasserstein Interpolation for Optimal Look-Ahead-Bias and Variance Tradeoff

TL;DR

This paper introduces a Wasserstein-based imputation method for time-series data that balances the trade-off between look-ahead bias and variance, improving out-of-sample performance in practical applications.

Contribution

It proposes a Bayesian posterior consensus distribution leveraging Wasserstein interpolation to optimally manage bias-variance trade-off in time-series imputation.

Findings

Reduces look-ahead bias in financial data imputation

Improves out-of-sample predictive accuracy

Demonstrates effectiveness on synthetic and real datasets

Abstract

Missing time-series data is a prevalent practical problem. Imputation methods in time-series data often are applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, in finance, imputation of missing returns may be applied prior to training a portfolio optimization model. Unfortunately, this practice may result in a look-ahead-bias in the future performance on the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian posterior consensus distribution which optimally controls the variance and look-ahead-bias trade-off in the imputation. We demonstrate the benefit of our methodology both in synthetic and real financial data.