Fig. 1
From: Determining the chaotic behaviour of copper prices in the long-term using annual price data
Annual copper real prices base 2012 = 100. a Evolution between 1900 and 2015 flagged by major price state and trends. Data includes remarkable economic and financial events in the period (Hong et al., 1996; Radetzki, 2009; Slade, 2015; Tapia Cortez et al., 2017; The Federal Reserve, 2017). During the first 18 years, prices sharply rise for 4 years until reaching the maximum value. Then, prices fall for longer periods and remain fluctuating at low level until the next price rising attempt. The next price rally extended for 3 years whereupon prices fall dramatically to the lowest level of the time series. Low prices during the following 44 years shows that three sharp price rising trends evolving between three to 5 years. After reaching the maximum value of the rally, prices strongly decrease and remain fluctuating at low level for about eight to 10 years. This is a similar pattern exhibited during high prices period; however, it is much longer. High price pattern repeats between 1964 and 1975 exhibiting the two price rise attempts followed by the sharp falls. Then, between 1975 and 2005, low price pattern comes back showing the three short prices growing periods followed by larger price decreasing and fluctuation periods. Finally, between 2006 and 2015 the high prices dynamic is repeated. The two price ascents evolved in a shorter period; however, the characteristic sudden prices decline is also displayed. b Time delay plot (τ = 1, m = 2) and (c) Time delay plot (τ = 2, m = 2). Values heuristically chosen. As the scale of the time series is annual (Δt = 1 year), τ = 1 and τ = 2 are small enough and appropriate to cover the dynamics of the system were the effects of changes of main macroeconomic variables can be perceived in the economy at from three quarter up to 6 years (Alquist and Kilian, 2010; Bernanke, 2013, 2010; Calvo, 2008; Frankel, 2014; Friedman, 1988, 1968; Gürkaynak et al., 2005; Hoover, 1985; Lederman and Maloney, 2007; Yellen, 2013). In both cases, τ = 1 and τ = 2, we identify five trails named TS_01, TS_02, TS_03, TS_04 and TS_05 which are grouped in two states: low-prices (TS_02 and TS_04) and high-prices (TS_01, TS_03 and TS_05)
