Controversy in financial chaos research and nonlinear dynamics: A short literature review

Multifractal Dynamics and Complexity Transformation in the Tanker Freight Market

“…From Figure 4 (a) and (c), both the BCTI and BDTI markets are with multifractal characteristics though they are different from the specific routes of TC2 and TD7 in Figure 4 (b) and (d). According to references, big events such as global financial crisis can lead to structural breaks in time series [44][45][46], we divide the sample data BDTI into two parts: period I from Jan 28, 1998 to Dec 01, 2010 and period II from Dec 02, 2010 to Jan 12, 2024 to delve into the changing external factors' effects on the multifractalities.…”

“…The study of multifractal time series often involves various scaling exponents, among which the q-order Hurst exponent Hq is prominent. However, the local Hurst exponent Ht has proven advantageous in detecting specific time points of structural change within a time series [44][45][46][47][48][49][50]. This local perspective aligns with q-order Hurst Hq values for extreme fluctuations, correlating positively or negatively depending on the q value's sign.…”

“…These time series analyses delve into the interplay between numerous variables affecting freight rates, such as crude oil prices, charter rates, fleet size, and policy changes, aiming to enhance forecasting models and risk management practices within the shipping industry [35][36][37][38][39][40]. Multifractal analysis has emerged as a new trend in these studies，gaining traction due to its ability to capture the asymmetric nature of market risks, demonstrating different magnitudes of response to upward and downward trends and uncovers various scaling behaviors within the data [41][42][43][44][45][46]. Henceforth our discussion will try to recognize the freight rates which exhibit a spectrum of fractal characteristics, not just a single pattern of fluctuations.…”