A Chaos Analysis of the Dry Bulk Shipping Market

• Main Authors: Lucía Inglada-Pérez, Pablo Coto-Millán
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Mathematics
• Subjects: chaos; nonlinear dynamics; correlation dimension; Lyapunov exponent; recurrence plots; GARCH
• Online Access: https://www.mdpi.com/2227-7390/9/17/2065

Finding low-dimensional chaos is a relevant issue as it could allow short-term reliable forecasting. However, the existence of chaos in shipping freight rates remains an open and outstanding matter as previous research used methodology that can produce misleading results. Using daily data, this paper aims to unveil the nonlinear dynamics of the Baltic Dry Index that has been proposed as a measure of the shipping rates for certain raw materials. We tested for the existence of nonlinearity and low-dimensional chaos. We have also examined the chaotic dynamics throughout three sub-sampling periods, which have been determined by the volatility pattern of the series. For this purpose, from a comprehensive view we apply several metric and topological techniques, including the most suitable methods for noisy time series analysis. The proposed methodology considers the characteristics of chaotic time series, such as nonlinearity, determinism, sensitivity to initial conditions, fractal dimension and recurrence. Although there is strong evidence of a nonlinear structure, a chaotic and, therefore, deterministic behavior cannot be assumed during the whole or the three periods considered. Our findings indicate that the generalized autoregressive conditional heteroscedastic (GARCH) model and exponential GARCH (EGARCH) model explain a significant part of the nonlinear structure that is found in the dry bulk shipping freight market.