A Semi-Parametric Non-linear Neural Network Filter: Theory and Empirical Evidence

In this work, we decompose a time series into trend and cycle by introducing a novel de-trending approach based on a family of semi-parametric artificial neural networks. Based on this powerful approach, we propose a relevant filter and show that the proposed trend specification is a global approximation to any arbitrary trend. Furthermore, we prove formally a famous claim by Kydland and Prescott (1981, 1997) that over long time periods, the average value of the cycles is zero. A simple procedure for the econometric estimation of the model is developed as a seven-step algorithm, which relies on standard techniques, where all relevant measures may be computed routinely. Next, using relevant DGPs, we compare and show by means of Monte Carlo simulations that our approach is superior to Hodrick–Prescott (HP) and Baxter and King (BK) regarding the generated distortionary effects and the ability to operate in various frequencies, including changes in volatility, amplitudes and phase. In fact, while keeping the structure of the model relatively simple, our approach is perfectly capable of addressing the case of stochastic trend, in the sense that the generated distortionary effects in the near unit root case are minimal and, by all means, considerably fewer than those generated by HP and BK. Application to EU15 business cycles clustering is presented and the empirical results are consistent with the rigorous theoretical framework developed in this work.