  Systems with stochastic time delay between the input and output present a
number of unique challenges. Time domain noise leads to irregular alignments,
obfuscates relationships and attenuates inferred coefficients. To handle these
challenges, we introduce a maximum likelihood regression model that regards
stochastic time delay as an "error" in the time domain. For a certain subset of
problems, by modelling both prediction and time errors it is possible to
outperform traditional models. Through a simulated experiment of a univariate
problem, we demonstrate results that significantly improve upon Ordinary Least
Squares (OLS) regression.
