Iranian Journal of Economic Research

Abstract 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.

Abstract The movements in oil prices are complex and, therefore, seem to be unpredictable. The traditional linear structural models have not been promising when applied to forecasting, particularly in the case of complex series such as oil prices. Although linear and nonlinear time series models have done much better job in forecasting oil prices, there is yet room for an improvement. If the data generating process is nonlinear, applying linear models could result in misleading forecasts. Model specification in nonlinear modeling can also be very case dependent and time-consuming.
   In this paper, we model and forecast daily futures oil price, listed in NYMEX, applying ARIMA, and GARCH models, for the period April June 1983 – Jan. 2003. Then, we test for chaos using BDS, Lyapunov exponent, Neural Networks, and Embedding Dimension methods. Finally, we will set up a nonlinear and flexible ANN model to forecast the series. Since the tests for chaos indicate that the oil price in futures markets is chaotic, the ANN model should make better forecasts. The forecasts comparison among the models approves that.  

Abstract Chaos theory is rather new in science, but, it is, in fact, rooted in ancients' perception of the world. The main idea is that although a complex system, such as world, seems to be generated by a random, and therefore, unpredictable process, it may run by a nonlinear deterministic process. Chaos theory has been applied to some Economic time series to see if they have an order, and, therefore, predictable. Some Economic time series, such as stock prices, look random, but, according to the chaos theory, they may come from a nonlinear deterministic process. If the data generating process is nonlinear, using traditional linear methods in estimation and forecasting can be misleading. Chaos theory is also applied to macroeconomic models. Some macroeconomic concepts, such as endogenous business cycles, can now be explained by the theory. In this paper, I try to review the chaos theory and its mathematical root for economists. Then, I will survey the Economic applications of the theory, and finally, will analyze different methods introduced for testing for chaos.