Title: Complexity of products: the effect of data regularisation,
Abstract: Among several developments, the field of Economic Complexity (EC) has notably
seen the introduction of two new techniques. One is the Bootstrapped Selective
Predictability Scheme (SPSb), which can provide quantitative forecasts of the
Gross Domestic Product of countries. The other, Hidden Markov Model (HMM)
regularisation, denoises the datasets typically employed in the literature. We
contribute to EC along three different directions. First, we prove the
convergence of the SPSb algorithm to a well-known statistical learning
technique known as Nadaraya-Watson Kernel regression. The latter has
significantly lower time complexity, produces deterministic results, and it is
interchangeable with SPSb for the purpose of making predictions. Second, we
study the effects of HMM regularization on the Product Complexity and logPRODY
metrics, for which a model of time evolution has been recently proposed. We
find confirmation for the original interpretation of the logPRODY model as
describing the change in the global market structure of products with new
insights allowing a new interpretation of the Complexity measure, for which we
propose a modification. Third, we explore new effects of regularisation on the
data. We find that it reduces noise, and observe for the first time that it
increases nestedness in the export network adjacency matrix.