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.

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.

The term structure of interest rates is a fundamental decision–making tool for various economic activities. Despite the huge number of contributions in the field, the development of a reliable framework for both fitting and forecasting under various market conditions (either stable or very volatile) still remains a topical issue. Motivated by this problem, this study introduces a methodology relying on optimal time–varying parameters for three and five factor models in the Nelson–Siegel class that can be employed for an effective in-sample fitting and out–of–sample forecasting of the term structure. In detail, for the in–sample fitting we discussed a two–step estimation procedure leading to optimal models parameters and evaluated the performances of this approach in terms of flexibility and fitting accuracy gains. For what it concerns the forecasting, we suggest an approach overcoming the well–known issue between the stability of factor models’ parameters and the optimal dynamic decay terms. To such aim, we use either autoregressive or machine learning techniques as local data generating processes based on the optimal parameters time series derived in the in–line fitting step. The so–obtained values are then employed to get day–ahead predictions of the yield curve. We assessed the proposed framework on daily spot rates of the BRICS (Brazil, Russia, India, China and South Africa) bond market. The experimental analysis illustrated that (i) time–varying parameters ensure a significant boost in the models fitting power and a more faithful representation of the yield curves dynamics; (ii) the proposed approach provides also stable and accurate predictions.