Chaotic Process in The Tehran Stock Price Index

The very complex movements in the stock prices are usually taken as random or stochastic, but they may be produced by a deterministic data generating process. Chaos refers to the nonlinear dynamic deterministic process that generates a series, which appears like random, but has a long memory. In the Economics and Finance literature, stock prices are known to be random due to their complexities, and therefore being unpredictable. In this paper, we test for chaos in the stock prices using the data from the daily and weekly stock prices listed in the Tehran Exchange Market (TEPIX) in 1377-1382 (1998-2003). We apply three tests for chaos, namely; BDS, Lyaponov Exponent, and Neural Networks; to the residuals of linear (ARIMA) and nonlinear (GARCH) models. The BDS and the Neural Networks tests results show that there exists nonlinearity in the ARIMA residuals, but not in the GARCH residuals. However, the Lyaponove exponent test result is positive for all different dimensions indicating that the TEPIX is chaotic.