股票波动率模拟及对中国市场预测效果的实证研究

利用实际波动率衡量标准和损失函数评价指标对GARCH类模型的波动率进行模拟并对中国市场的预测效果进行了实证研究,得出:1)在模拟期,EGARCH模型的模拟效果相对最优;2)在预测期,没有一个模型的预测效果表现相对出色;3)以实际波动率为标准,模拟和预测效果均显得不足,预测效果更是不容乐观.     

Volatility forecasting via SVR–GARCH with mixture of Gaussian kernels

The support vector regression (SVR) is a supervised machine learning technique that has been successfully employed to forecast financial volatility. As the SVR is a kernel-based technique, the choice of the kernel has a great impact on its forecasting accuracy. Empirical results show that SVRs with hybrid kernels tend to beat single-kernel models in terms of forecasting accuracy. Nevertheless, no application of hybrid kernel SVR to financial volatility forecasting has been performed in previous researches. Given that the empirical evidence shows that the stock market oscillates between several possible regimes, in which the overall distribution of returns it is a mixture of normals, we attempt to find the optimal number of mixture of Gaussian kernels that improve the one-period-ahead volatility forecasting of SVR based on GARCH(1,1). The forecast performance of a mixture of one, two, three and four Gaussian kernels are evaluated on the daily returns of Nikkei and Ibovespa indexes and compared with SVR–GARCH with Morlet wavelet kernel, standard GARCH, Glosten–Jagannathan–Runkle (GJR) and nonlinear EGARCH models with normal, student-t, skew-student-t and generalized error distribution (GED) innovations by using mean absolute error (MAE), root mean squared error (RMSE) and robust Diebold–Mariano test. The results of the out-of-sample forecasts suggest that the SVR–GARCH with a mixture of Gaussian kernels can improve the volatility forecasts and capture the regime-switching behavior.     

Fuzzy finite element model updating of the DLR AIRMOD test structure

This article presents the application of finite-element fuzzy model updating to the DLR AIRMOD structure. The proposed approach is initially demonstrated on a simulated mass-spring system with three degrees of freedom. Considering the effect of the assembly process on variability measurements, modal tests were carried out for the repeatedly disassembled and reassembled DLR AIRMOD structure. The histograms of the measured data attributed to the uncertainty of the structural components in terms of mass and stiffness are utilised to obtain the membership functions of the chosen fuzzy outputs and to determine the updated membership functions of the uncertain input parameters represented by fuzzy variables. In this regard, a fuzzy parameter is introduced to represent a set of interval parameters through the membership function, and a meta model (kriging, in this work) is used to speed up the updating. The use of non-probabilistic models, i.e. interval and fuzzy models, for updating models with uncertainties is often more practical when the large quantities of test data that are necessary for probabilistic model updating are unavailable.     

Fuzzy confidence interval for pH titration curve

In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.     

Adaptive type-2 fuzzy backstepping control of uncertain fractional-order nonlinear systems with unknown dead-zone

A new problem of adaptive type-2 fuzzy fractional control with pseudo-state observer for commensurate fractional order dynamic systems with dead-zone input nonlinearity is considered in presence of unmatched disturbances and model uncertainties; the control scheme is constructed by using the backstepping and adaptive technique. To avoid the complexity of backstepping design process, the dynamic surface control is used. Also, Interval type-2 Fuzzy logic systems (IT2FLS) are used to approximate the unknown nonlinear functions. By using the fractional adaptive backstepping, fractional control laws are constructed; this method is applied to a class of uncertain fractional-order nonlinear systems. In order to better control performance in reducing tracking error, the PSO algorithm is utilized for tuning the controller parameters. Stability of the system is proven by the Mittag–Leffler method. It is shown that the proposed controller guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the origin. The efficiency of the proposed method is illustrated with simulation examples.     

A 2uFunction representation for non-uniform type-2 fuzzy sets: Theory and design

The theoretical and computational complexities involved in non-uniform type-2 fuzzy sets (T2 FSs) are main obstacles to apply these sets to modeling high-order uncertainties. To reduce the complexities, this paper introduces a 2uFunction representation for T2 FSs. This representation captures the ideas from probability theory. By using this representation, any non-uniform T2 FS can be represented by a function of two uniform T2 FSs. In addition, any non-uniform T2 fuzzy logic system (FLS) can be indirectly designed by two uniform T2 FLSs. In particular, a 2uFunction-based trapezoid T2 FLS is designed. Then, it is applied to the problem of forecasting Mackey–Glass time series corrupted by two kinds of noise sources: (1) stationary and (2) non-stationary additive noises. Finally, the performance of the proposed FLS is compared by (1) other types of FLS: T1 FLS and uniform T2 FLS, and (2) other studies: ANFIS [54], IT2FNN-1 [54], T2SFLS [3] and Q-T2FLS [35]. Comparative results show that the proposed design has a low prediction error as well as is suitable for online applications.     

沪深300仿真股指期货价格不对称跳跃波动的实证分析

本研究利用2006年10月30日至2009年3月13日期间的仿真的沪深300指数期货每日结算价,探讨了期货价格的不对称跳跃波动行为。在实证研究方法上,本文以Chan和Maheu的GARCH(1,1)-ARJI模型为基础并进行了扩展,以EGARCH(1,1)-CJI和EGARCH(1,1)-ARJI两种模型来刻画股指期货价格的不对称和跳跃波动行为。实证结果显示:(1)沪深300仿真股指期货价格存在不对称跳跃波动,而且跳跃强度不为一固定常数,异常信息所产生的跳跃强度是随着时间变动的。(2)经过似然比检验,结果显示EGARCH(1,1)-ARJI模型比EGARCH(1,1)-CJI模型具有更好的拟合能力。     

具有模糊目标的多目标双矩阵对策集结与求解

针对不确定性多冲突环境,建立了多个具有模糊目标的多目标双矩阵对策的综合集结模型.在假定局中人各模糊目标的隶属函数为线性函数的情形下,基于总体模糊目标的可达度,给出了纳什均衡解的定义,并应用粒子群优化算法对集结模型求解.最后,给出一个军事例子说明了模型的实用有效性和粒子群优化算法求解的高效性.     

不确定区间隶属度语言变量及其应用

基于不确定语言变量和区间模糊数,提出了不确定区间隶属度语言变量的概念,定义了不确定区间隶属度语言变量的运算规则、大小比较方法,给出了不确定区间隶属度语言变量的加权算术平均算子、加权几何平均算子及其相应性质,并将这些算子应用于属性权重确知且属性值以不确定区间隶属度语言变量形式给出的不确定多属性群决策问题中,通过示例验证了基于不确定区间隶属度语言变量信息的多属性群决策方法的有效性和可行性。     

Type-2 T–S fuzzy impulsive control of nonlinear systems

A novel impulsive control approach based on interval Type-2 T–S fuzzy model has been presented for nonlinear systems in this paper. This approach makes up for the drawback of Type-1 fuzzy impulsive control, which cannot fully handle the uncertainties in describing the complex nonlinear systems by Type-1 fuzzy membership functions and cannot give rigorous fuzzy rules. Further more, this approach uses the “broad band” effect of the Type-2 membership functions to solve the noise of training data and exterior disturbance of the Type-1 fuzzy impulsive control. By using Lyapunov theory and Lipschitz condition, which is combined with integrated approaches such as comparison methods and linear matrix inequalities, the Type-2 fuzzy impulsive controller is designed and the general asymptotical stability analysis of the systems is given. Finally, the simulation of the inverted pendulum model demonstrates the validity and superiority of the proposed method by easily determining the membership functions and choosing minimum number of fuzzy rules and the method can handle random disturbance and data uncertainties very well.     

Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost

In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP). In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic) membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.     

基于直觉模糊化的广义模糊时间序列预测模型

本文在传统广义模糊时间序列预测模型数据模糊化的基础上,引入直觉模糊集理论对其进行扩展。首先,在隶属度和非隶属度函数中增加犹豫度因子对样本数据进行直觉模糊化,更加细腻的反映数据不确定性本质。然后,用记分函数描述样本数据对模糊集的隶属情况,简化模型的复杂度。随后以传统广义模型为框架,构建基于直觉模糊化的广义模糊时间序列预测模型。最后利用典型的Alabama大学入学人数为实验数据,对比分析本文建立模型与传统广义模型的预测结果,验证直觉模糊化的广义模糊时间序列模型的可行性和优越性。     

New fuzzy wavelet network for modeling and control: The modeling approach

In this paper, a fuzzy wavelet network is proposed to approximate arbitrary nonlinear functions based on the theory of multiresolution analysis (MRA) of wavelet transform and fuzzy concepts. The presented network combines TSK fuzzy models with wavelet transform and ROLS learning algorithm while still preserve the property of linearity in parameters. In order to reduce the number of fuzzy rules, fuzzy clustering is invoked. In the clustering algorithm, those wavelets that are closer to each other in the sense of the Euclidean norm are placed in a group and are used in the consequent part of a fuzzy rule. Antecedent parts of the rules are Gaussian membership functions. Determination of the deviation parameter is performed with the help of gold partition method. Here, mean of each function is derived by averaging center of all wavelets that are related to that particular rule. The overall developed fuzzy wavelet network is called fuzzy wave-net and simulation results show superior performance over previous networks.The present work is complemented by a second part which focuses on the control aspects and to be published in this journal([17]). This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems.     

Approximation of centroid end-points and switch points for replacing type reduction algorithms

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik–Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process.     

基于GARCH模型族的中国股市波动性预测

收益与风险历来都是投资者与研究者所关注的问题 .本文选取 GA RCH、TGARCH和 EGARCH模型来拟合中国股市的波动性 .实证分析结果表明 ,中国股市的波动具有显著的波动聚类性与持续性 ;由 E-GARCH模型所预测的上证 30指数、上证综合指数和深证成份指数未来一天的波动要明显优于 GARCH和TGARCH模型的对应值 ,而对香港恒生指数 ,三种模型的预测结果无显著的差异 .     

考虑微观结构噪声与跳跃影响的波动建模

现有的金融高频数据研究,并未充分考虑微观结构噪声对波动建模和预测的影响.以非参数化方法为理论框架,基于高频数据,采用适当方法分离出波动中的微观结构噪声成份,构建了新的跳跃方差和连续样本路径方差,将已实现波动分解为连续样本路径方差、跳跃方差和微观结构噪声方差.同时考虑微观结构噪声和跳跃对波动的影响,对HAR-RV-CJ模型进行改进,提出了HAR-RV-N-CJ模型和LHAR-RV-N-CJ模型.通过上证综指高频数据进行实证,结果表明新模型在模型拟合和预测方面均优于HAR-RV-CJ模型.     

基于TFWPA算子的模糊优化组合预测模型及其应用

传统的组合预测中,预测对象往往是实数或区间数,实际上,三角模糊数则更能刻画不确定环境下复杂事物的某些量的特征。因此,本文提出一种预测信息为三角模糊数的模糊优化组合预测新方法。定义了两个三角模糊数的相对误差,同时考虑到预测数据之间的交叉影响,基于三角模糊加权Power平均(TFWPA)算子、三角模糊加权Power几何(TFWPG)算子和max-min准则,分别构建模糊优化组合预测模型。提出非劣性和优性组合预测的概念,证明所提模糊组合预测模型具有非劣性质。最后通过实例分析说明了该模糊组合预测方法的有效性,并对参数做了灵敏度分析。     

A novel two-factor forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling vague and incomplete data. A variety of forecasting models have devoted to improving forecasting accuracy, however, the issue of partitioning intervals has rarely been investigated. Recently, we proposed a novel deterministic forecasting model to eliminate the major overhead of determining the k-order issue in high-order models. This paper presents a continued work with focusing on handling the interval partitioning issue by applying the fuzzy c-means technology, which can take the distribution of data points into account and produce unequal-sized intervals. In addition, the forecasting model is extended to allow process twofactor problems. The accuracy superiority of the proposed model is demonstrated by conducting two empirical experiments and comparison to other existing models. The reliability of the forecasting model is further justified by using a Monte Carlo simulation and box plots. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization

In real time, one observation always relies on several observations. To improve the forecasting accuracy, all these observations can be incorporated in forecasting models. Therefore, in this study, we have intended to introduce a new Type-2 fuzzy time series model that can utilize more observations in forecasting. Later, this Type-2 model is enhanced by employing particle swarm optimization (PSO) technique. The main motive behind the utilization of the PSO with the Type-2 model is to adjust the lengths of intervals in the universe of discourse that are employed in forecasting, without increasing the number of intervals. The daily stock index price data set of SBI (State Bank of India) is used to evaluate the performance of the proposed model. The proposed model is also validated by forecasting the daily stock index price of Google. Our experimental results demonstrate the effectiveness and robustness of the proposed model in comparison with existing fuzzy time series models and conventional time series models.     

Fuzzy pricing,marketing and service planning in a fuzzy inventory model: A geometric programming approach

In the real world markets, demand is influenced by different parameters. Recently, many researchers have been interested in integrated production and marketing planning strategies in inventory models where demand depends on different parameters such as price and/or marketing expenditure. The quality of services that are offered to customers of a product is one of the most important parameters that affects demand in the real markets and has not been considered in development of inventory models. On the other hand, the cost parameters in real inventory systems and other parameters such as price, marketing and service elasticity to demand are imprecise and uncertain in nature. So, the notion of fuzziness can be applied to cope with this uncertainty. In this paper, a new fuzzy profit maximization inventory model with shortages is proposed. The demand is considered as a power function of price, marketing expenditure and service expenditure. Furthermore, unit cost is determined as a power function of order quantity. Since the proposed model is in a fuzzy environment, a fuzzy decision should be made to meet the decision criteria, and the results should be fuzzy. Therefore, the proposed model is formulated and solved using geometric programming and fuzzy optimization techniques to derive an approximation of the results’ membership functions. The model is illustrated with a numerical example and finally a case study is provided for evaluation and validation of the results of model.