Equation Discovery for Macroeconomic Modelling

This article describes a machine learning based approach applied to acquiring empirical forecasting models. The approach makes use of the LAGRAMGE equation discovery tool to define a potentially very wide range of equations to be considered for the model. Importantly, the equations can vary in the number of terms and types of functors linking the variables. The parameters of each competing equation are automatically fitted to allow the tool to compare the models. The analysts using the tool can exercise their judgement twice, once when defining the equation syntax, restricting in such a way the search to a space known to contain several types of models that are based on theoretical arguments. In addition, one can use the same theoretical arguments to choose among the list of best fitting models, as these can be structurally very different while providing similar fits on the data. Here we describe experiments with macroeconomic data from the Euro area for the period 1971–2007 in which the parameters of hundreds of thousands of structurally different equations are fitted and the equations compared to produce the best models for the individual cases considered. The results show the approach is able to produce complex non-linear models with several equations showing high fidelity.