《Table 2 BDS independence test results》

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《"The chaotic behavior among the oil prices, expectation of investors and stock returns: TAR-TR-GARCH copula and TAR-TR-TGARCH copula"》

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The results are reported in Table 4.The Kolmogorov entropy for oil price is 0.147.According to this result，the timescale of a rational and effective forecast for that system must be within*68 days.This result is different to the He（2011）who found that the system should be within36 days by using the Kolmogorov entropy.