“…https://orcid.org/0000-0002-4452-1540 Notes a. In addition, we applied the BDS test 71 to the 10 steel price series and found that the p-values of the tests are all almost zero based on embedding dimensions of 2-10 and ϵ (distance used to test proximity of data points) values of 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0 times the price series standard deviation, [72][73][74][75][76][77][78][79] indicating some non-linear patterns as found in many different commodity prices. 80-85 b. p = 10 and X t = (X 1,t X 2,t X 3,t X 4,t X 5,t X 6,t X 7,t X 8,t X 9,t X 10,t ) ′ in our example, where X 1,t , X 2,t , X 3,t , X 4,t , X 5,t , X 6,t , X 7,t , X 8,t , X 9,t and X 10,t are related to prices of the rebar, steel wire, plate, hot rolled coil, cold rolled plate, galvannealed sheet, seamless tube, welded tube, section and narrow strip, respectively.…”