مدل گراف فازی به کار گرفته شده در سناریوی بازار سهام با استفاده از الگوریتم ژنتیک

In this paper, we derive a new application of fuzzy systems designed for a generalized autoregression conditional heteroscedasticity (GARCH) model. In general, stock market performance is time-varying and nonlinear, and exhibits properties of clustering. The latter means simply that certain large changes tend to follow other large changes, and in general small changes tend to follow other small changes. This paper shows results from using the method of functional fuzzy systems to analyze the clustering in the case of a GARCH model. The optimal parameters of the fuzzy membership functions and GARCH model are extracted using a genetic algorithm (GA). The GA method aims to achieve a global optimal solution with a fast convergence rate for this fuzzy GARCH model estimation problem. From the simulation results, we have determined that the performance is significantly improved if the leverage effect of clustering is considered in the GARCH model. The simulations use stock market data from the Taiwan weighted index (Taiwan) and the NASDAQ composite index (NASDAQ) to illustrate the performance of the proposed method.

In analyzing time-dependent data, it is often the case that the conditional variances are not consistent with the assumption of homogeneity that is commonly associated with traditional econometrics models, especially those which treat financial data (Arciniegas and Rueda, 2008, Chan, 2002, Fama, 1965 and Tsay, 2002). Mandelbrot (1963) discovered that conditional variance plays a role is in the phenomenon of volatility clustering. Volatility clustering means that large changes tend to follow other large changes, and small changes tend to follow small changes. Because of this phenomenon, Mandelbrot thought that the variance might change over time, that is, it would not be constant or homogeneous. Therefore, Engle (1982) proposed the autoregression conditional heteroscedasticity (ARCH) construct. Engle believed that conditional variances led to assumption of homogeneity. However, this approach proved impractical. He subsequently adopted a model in which conditional variances in time-dependent data were subject to influences from previous unexpected factors. Furthermore, he assumed that the conditional variances were functions of error terms, allowing them to change over time. He proposed that the ARCH Model could solve the biases and therefore address traditional econometrics models.

Empirical evidence demonstrates that the financial market data that we used is nonlinear and time-variance. For these reasons, this paper proposes a new method that we call the fuzzy GARCH model, a very nonlinear and highly complex approach. We used a GA-based design method to estimate parameters for the fuzzy GARCH model. Our simulation results indicate that the proposed method offers significant performance improvements. Furthermore, the GA algorithm was able to search for peaks parallel to the parameter space, and it was therefore not necessary to specify any initial conditions in order to achieve improved results.