چکیده:
Modeling and analysis of future prices has been hot topic for economic analysts in recent years. Traditionally, the complex movements in the prices are usually taken as random or stochastic process. However, they may be produced by a deterministic nonlinear process. Accuracy and efficiency of economic models in the short period forecasting is strategic and crucial for business world. Nonlinear models are efficient enough and suitable for short time forecasting. So notable attempts is devoted on understanding different economic time series’ and nonlinear dynamical models that can fit them.
In this paper, it is tried to investigate Tehran stock exchange index time series. It is assumed. So, the Correlation Dimension (CD), the Hurst Exponent, and the Largest Lyapunov Exponent (LLE) of the time series are calculated. It is shown that the time series corresponding to Tehran stock Exchange index is nonlinear. The analyses of the results show enough evidence to accept the conjecture of existence chaotic behavior in Tehran stock exchange index
خلاصه ماشینی:
"Many researchers, such as Scheinkman & LeBaron (1989 a,b), Blank (1991), Hsieh (1991), DeCoster (1992), Yang and Brorsen (1993), Fang (1994), Kohzadi (1995), Panas, E.
We use the following tests to investigate Tehran stock exchange index: Hurst Exponent, Correlation Dimension (CD) and Largest Lyapunov Exponent (LLE).
(Sprott, 2003) Correlation dimension can be calculated using the distances between each pair of points in the set of N number of points, (Grassberger and Procaccia 1983) A correlation function, C(r), is then calculated using, C(r) has been found to follow a power law: Therefore, we can find Dcorr with estimation techniques derived from the formula: C(r) can be written in a more mathematical form as where is the Heaviside step function described as, To get sure of chaotic structure it is better to apply CD on residue value of Auto Regression model (Brock W.
The CD‘s of Tehran Stock Exchange Index The correlation dimension for daily, weekly, and monthly data are shown in Figures 5 to Figure 7 respectively.
The LLE of Tehran Stock Exchange Index The result of calculation for LLE on Daily, Weekly and monthly data are shown in Table 4, to Table 6 and Figure 8, to Figure 14.
By calculating the Hurst exponent and correlation dimension, it may be found that time series corresponding to Tehran stock exchange index may be considered as nonlinear deterministic series.
It may be concluded that for forecasting in Tehran stock exchange index nonlinear and deterministic models could be more reliable, Richness of nonlinear models to interpret the behavior of time series could help researcher to understand underlying phenomena in the market."