Least Squares-Optimal Transport (LS-OT) Regression for varying time delays

An enhancement to OLS regression for varying time lagged information transmission between the independent and dependent variables

Abstract

While analysing time series data, conventional linear regression methods leave us the choice with one of two assumptions: either the dependent and independent variables are synchronous or fixed time lags are assumed.

However the time lag might be varying over time, or noisy. The time lag becomes an additional source of error beside the usual (measurement) noise. Ignoring the variable time lag amounts to a specification error. We propose to use optimal transport cost as a way to account for the time lag uncertainty and make ordinary least squares (OLS) robust to this type of specification error.  This enhancement to the celebrated OLS regression model of noise easily generalises to multivariate regression, and alternative models such as Partial Least Square.