Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process

Stochastic models traditionally used to describe metals’ prices have proved not to be suitable to represent the dynamic behavior and time-related nature of metal markets. Rates of return are characterized by non-Gaussian and heterogeneous characteristics, which requires the use of properly adjusted models. In this paper, we introduce a stochastic model that takes under consideration the mentioned specific characteristics of the real data corresponding to the mineral commodity prices, namely the non-homogeneous character (time-dependent characteristics) and non-Gaussian distribution. The introduced model is in some sense the extension of the classical Ornstein–Uhlenbeck process (called also the Vasicek model) which was originally used to the interest rate data description. The proposed in this paper model, in contrast to the classical process, has the time-dependent parameters. This perfectly captures the time-dependent characteristics of the real data. Moreover, it is based on the general class of the skewed Student’s t-distribution (SGT), which is related to the non-Gaussian behavior of the real metals’ prices. This paper is a continuation of the authors’ previous research where the simpler model (Chan–Karolyi–Longstaff–Sander, CKLS) based on the SGT distribution was proposed. We demonstrate here the step-by-step procedure of the time-dependent parameters’ estimation and check its effectiveness by using the simulated data. Finally, based on the real-time series analysis, we demonstrate that the proposed stochastic model is universal and can be applied to metals’ prices description for the long-term prediction.