A Chaos Analysis of the Dry Bulk Shipping Market

Abstract

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.

A Study on the Nature of Complexity in the Spanish Electricity Market Using a Comprehensive Methodological Framework

“…The methodology used is built upon the one introduced by Inglada-Perez [25,26], encompassing these steps:…”

“…The plot is constructed supposing that mutual distances belong to the same trajectory in the reconstructed phase space. It is obtained from the recurrence matrix [50] whose construction is performed using the following algorithm [25,51]:…”

“…The overall methodological framework of this work is based on the one proposed by Inglada-Pérez [25,26] which has been specifically extended for this research by incorporating the following processes, among others: (i) the possible existence of seasonality in the time series that could affect the results and conclusions of the study is analyzed; (ii) the Lagrange multiplier test is incorporated to contrast whether the presence of nonlinearity is due to the existence of heteroscedasticity; and (ii) in the stage of the detection of a chaotic regime, the methodological tool of Recurrence Quantification Analysis is introduced, which, through the determination of several ratios, apart from providing information on other characteristics of the series, due to its quantitative nature, significantly improves the power of the recurrence plots to detect the existence of chaos. In summary, the methodological process is as follows:…”

A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

“…In the process of studying chaotic systems, an increasing number of complex dynamic properties have been introduced, such as hidden attractor, multistability, extreme multistability, and transient chaos [11][12][13]. These complex dynamics have been extensively used in many aspects [14][15][16][17][18].…”

Nonlinear Time Series Analysis in Unstable Periodic Orbits Identification-Control Methods of Nonlinear Systems

“…However, the quality of reconstruction depends on the choice of reconstruction parameters, size and delay. Now, with the reconstructed phase space [16][17][18], it is possible to analyze the dynamics of nonlinear systems using the recurrence plot method, which is a two-dimensional representation of the recurrences of the states of a system [19][20][21]. This method can highlight hidden correlations in the system through the presence of textures that are related to typical behaviors in terms of system dynamics [22,23].…”