Fig. 4

Statistical properties for the return process of the Sun Paper and return process generated by BS, CEV, GARCH, FinGAN-MLP, FinGAN-LSTM and FinGAN models. (a) Linear unpredictability is shown as the zero level of the auto-correlation function of the price return is at zero level for all lags. (b) Fat-tailed distribution is demonstrated by the power-law decay of the tails of the probability distribution. (c) Volatility clustering is expressed by the slow decay of the auto-correlation function for the absolute values of the price return. (d) Leverage effects are shown as the lead-lag correlation of the price return and the price volatility. (e) Coarse-fine volatility correlation is shown as the lead-lag correlation of the coarse and the fine volatility. (f) Gain/loss asymmetry is shown in the difference of the probability distributions for the time-step required to reach a certain positive (red) and negative (blue) price change. The sample period is from November 16, 2006 through June 30, 2021 and includes 3,556 observations