استفاده از سیستم های فازی ترکیب شده و مدل گارچ برای صورت انطباقی پیش بینی نوسانات بازار سهام

This paper studies volatility forecasting in the financial stock market. In general, stock market volatility is time-varying and exhibits clustering properties. Thus, this paper presents the results of using a fuzzy system method to analyze clustering in generalized autoregressive conditional heteroskedasticity (GARCH) models. It also uses the adaptive method of recursive least-squares (RLS) to forecast stock market volatility. The fuzzy GARCH model represents a joint estimation method; the membership function parameters together with the GARCH model parameters make this problem of stock market is highly nonlinear and complicated. This study presents an iterative algorithm based on a genetic algorithm (GA) to estimate the parameters of the membership functions and the GARCH models. In this paper, the GA method is employed to identify a global optimal solution with a fast convergence rate in the context of the fuzzy GARCH model estimation problem studied here. Based on simulation results, we determined that both the estimation of in-sample and the forecasting of out-of-sample volatility performance are significantly improved when the GARCH model considers both the clustering effect and the adaptive forecast.

Recently, there has been growing interest in modeling and forecasting volatility in the financial and economic literatures [1], [2], [3], [4], [5], [6], [7] and [8]. The seminal paper of Engle [9] proposed the autoregressive conditional heteroskedasticity (ARCH) construct. Bollerslev [10], a student of Engle, employed the autoregressive moving average (ARMA) model to introduce the generalized autoregressive conditional heteroskedasticity (GARCH) model in a 1986 Journal of Econometrics article. The GARCH model involves the joint estimation of a conditional mean and conditional variance equation; it is characterized by a fat tail and excess kurtosis. This model is also a weighted average of past squared residuals, but it has declining weights that never completely reach zero. The model provides parsimonious models that are easy to estimate and have proven to be surprisingly successful in predicting conditional variances. For these reasons, GARCH model is regularly used in analyzing the daily returns of stock market data. However, financial assets are easily impacted by both positive and negative information, and these impacts are often asymmetric. The GARCH model does not recognize the transmissions of volatility that come from the input of positive or negative information. Therefore, this model is not appropriate when the market is asymmetric. To overcome these shortcomings, GARCH has been extended in numerous ways. The GJR-GARCH model was developed by Glosten et al. [11], while the exponential GARCH (EGARCH) was proposed by Nelson [12]. These models suggest that the negative relationship between volatility and stock prices can be understood by the fact that an increase in unexpected volatility will increase expected future volatility, assuming persistence. Some of these effects can be captured by modifications of linear models, while others demand nonlinear approaches. Unfortunately, due to their complexity, nonlinear models are in very limited use today [1]. Considering these difficulties, there is currently demand for more flexible model. In this paper, we propose a fuzzy GARCH model based on fuzzy systems [13], [14], [15], [16] and [17]. Fuzzy modeling methods are promising techniques for describing complex dynamics and asymmetries in systems. Combining the ease of implementation and convenience of linear models with an ability to capture complex system correlations, we propose that fuzzy models can also be a judicious choice for analyzing both temporal asymmetries and persistence. In this paper, we combine GARCH models and fuzzy systems to develop a fuzzy GARCH model. We then apply this new model to real-world financial markets. The process of optimizing fuzzy systems and GARCH model parameters is highly complex and nonlinear. A GA-based parameter estimation algorithm is proposed to derive the optimal solution for the fuzzy GARCH model. GA methods are an approach to optimizing machine learning algorithms inspired by the processes of natural selection and genetic evolution [18] and [19]. A GA applies operators to a population of binary strings that encode the parameter space. A parallel global search technique emulates natural genetic operators such as reproduction, crossover, and mutation. At each generation, the algorithm explores different areas of the parameter space and then directs the search to the region where there is a high probability of finding improved performance. Because GA simultaneously evaluates many points in a parameter space, it is more likely to converge on the optimal solution [18], [20] and [21]. In particular, there is no requirement that the search space is differentiable or continuous, and the algorithm can be iterated several times for each data point. Accordingly, it is a very suitable approach for time-varying functions. In practice, in-sample parameter estimation schemes commonly assume a certain volatility model structure for financial stocks [2] and [5]. Hence, it is necessary to use an adaptive parameter estimation scheme applicable to general out-of-sample volatility models. In this paper, we use the out-of-sample forecast volatility of financial stocks with RLS as an adaptive algorithm in order to track changes in volatility. The rest of this paper is organized as follows. The next section describes the fuzzy GARCH model. Section 3 presents details on the adaptive forecasting algorithm. Experimental results illustrating the effectiveness of the proposed method are provided in Section 4. The final section of the paper concludes.

In this paper, we examine the predictive abilities of four classes of volatility models by comparing the forecasts with realized volatility measures as defined in Eq. (22). The adaptive fuzzyGARCH model appears to be advantageous when attempting to model the dynamics of high-frequency, time-varying volatility. Empirical evidence demonstrates that the financial market data used are nonlinear and time-varying. For these reasons, this paper proposes a new method that called the adaptive fuzzy GARCH model, which is a nonlinear and highly complex approach. We used a GA-based design method to estimate parameters for the fuzzy GARCH model and used an adaptive algorithm to forecast the olatility of various financial markets. Our simulation results indicate that the proposed method offers significant improvements in forecasting performance. Furthermore, the GA algorithm was able to search for peaks parallel to the parameter spac. It was therefore not necessary to specify any initial conditions in order to achieve an improvement in results.