We compare parametric and machine learning techniques (namely: Neural Networks) for in–sample modeling of the yield curve of the BRICS countries (Brazil, Russia, India, China, South Africa). To such aim, we applied the Dynamic De Rezende–Ferreira five–factor model with time–varying decay parameters and a Feed–Forward Neural Network to the bond market data of the BRICS countries. To enhance the flexibility of the parametric model, we also introduce a new procedure to estimate the time varying parameters that significantly improve its performance. Our contribution spans towards two directions. First, we offer a comprehensive investigation of the bond market in the BRICS countries examined both by time and maturity; working on five countries at once we also ensure that our results are not specific to a particular data–set; second we make recommendations concerning modelling and estimation choices of the yield curve. In this respect, although comparing highly flexible estimation methods, we highlight superior in–sample capabilities of the neural network in all the examined markets and then suggest that machine learning techniques can be a valid alternative to more traditional methods also in presence of marked turbulence.

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This work studies the term structure dynamics in the natural gas futures market, focusing on the Dutch Title Transfer Facility (TTF) daily futures prices. At first, using the whole dataset, we compared the in-sample fitting performance of three models: the four-factor dynamic Nelson–Siegel–Svensson (4F-DNSS) model, the five-factor dynamic De Rezende–Ferreira (5F-DRF) model, and the B-spline model. Our findings suggest that B-spline is the method that achieves the best in-line fitting results. Then, we turned our attention to forecasting, using data from 20 January 2011 to 13 May 2022 as the training set and the remaining data, from 16 May to 13 June 2022, for day-ahead predictions. In this second part of the work we combined the above mentioned models (4F-DNSS, 5F-DRF and B-spline) with a Nonlinear Autoregressive Neural Network (NAR-NN), asking the NAR-NN to provide parameter tuning. All the models provided accurate out-of-sample prediction; nevertheless, based on extensive statistical tests, we conclude that, as in the previous case, B-spline (combined with an NAR-NN) ensured the best out-of-sample prediction.