Multi-Objective Evolutionary Optimization for Time Series Lag Regression

It is well-known that in some regression problems the effect of an independent variables on the dependent one(s) may be delayed; this phenomenon is known as lag. Lag regression is one of the standard techniques for time series explanation and prediction. However, using lagged variables to transform a multivariate time series so that a propositional algorithm such as a linear regression learner can be used requires to decide, at preprocessing time, which independent variables must be lagged and by how much. In this paper, we propose a novel optimization schema to solve this problem. We test our solution, implemented with a multi-objective evolutionary algorithm, on real data taken from a larger project that aims to construct an explanation model for the study of atmospheric pollution in the city of Wroc law (Poland).