Parity Regression Estimation

Multiple linear regression remains a foundational predictive methodology across a broad range of applications. We propose a novel regression framework that, rather than minimising the aggregate prediction error associated with the dependent variable, explicitly distributes the risk evenly across all model parameters. This approach provides a structural safeguard that is particularly suitable for data affected by substantial noise, as is often the case in time series environments characterised by regime shifts, structural breaks, and evolving trends. We provide a theoretical characterisation of our proposed estimator, named Parity Regression, and benchmark its analytical properties against existing penalised and shrinkage estimators in the literature. Both synthetic experiments and empirical applications demonstrate that the theoretical guarantees of the proposed method translate into enhanced out-of-sample forecasting stability in practice.