Chaotic trend possibility in the gold market

Abstract

In this study, the International market gold prices over the last 31 years were analyzed for trends by five different methods, linear trend analysis, ARMA analysis, Rescaled range analysis, attractor reconstruction and maximal Lyapunov Exponent, detrended fluctuation analysis. Unfortunately not all methods give consistent results. The linear analysis reveals three regions with different trends. This is not supported by the rescaled range or detrended fluctuation analysis results. The maximal Lyapunov exponent calculation reveals chaotic behavior. The detrended fluctuation analysis reveals behavior close to brown noise. This is not corroborated by the rescaled range analysis, which indicates anti persistent behavior. The ARMA model implies first differencing that indicates a strong underlying linear trend. Combining these results, one probable explanation is that the strong linear trend, (also corroborated by ARMA analysis) affects the rescaled range calculation, because of its dependence on extreme values. The detrended fluctuation analysis removes this trend and reveals brown noise. This is consistent with a maximal positive Lyapunov exponent. Hence, we have a linear trend plus brown noise and neither of these two effects is dominant. © 2020 Elsevier B.V., All rights reserved.