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In this article, we show that the memory of markets has nonchaotic behaviour. Its time trend is neutral and nonlinearity tests such as Brock, Dechert, Sheinkman (BDS) rejects nonlinearity in stock markets' memories. The estimation of fractional differencing parameters is carried out by various methods such as Maximum Likelihood Estimation (MLE), Nonlinear Least Squares (NLS), Hurst exponents, Gewek, Porter- Hudak (GPH), wavelet transformation, and Whittle. Also Lyapunov exponents are estimated by two methods of Rosenstein and Jacobian. Results of Lyapunov exponent estimation shows memory of markets are not chaotic. Furthermore, there are no any Autoregressive Conditional Heteroscedasticity (ARCH) effects in memory of markets. ARCH test is more specific than the BDS test and it may powerful test for detecting possible ARCH effects. All of tests show memory of markets has random behaviour.
