A Fuzzy Asymmetric GARCH model applied to stock markets

In this paper, we derive a new class of flexible threshold asymmetric Generalized Autoregression Conditional Heteroskedasticity (GARCH) models. We use this tool for analysis and modeling of the properties that are apparent in many financial time series. In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric GARCH model. Our simulations use stock market data from the Taiwan weighted index (Taiwan), the Nikkei 225 index (Japan), and the Hang Seng index (Hong Kong) to illustrate the performance of our proposed method. From the simulation results, we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the GARCH model.     

小波变换与GARCH组合模型的网络流量预测

在一些网络环境当中,网络流量具有非线性、异方差性和波动集群现象,传统的小波变换与ARMA组合模型不能很好地描述网络流量的这些特性。因此,研究使用了小波变换与广义自回归条件异方差GARCH组合模型来预测网络流量。首先,使用小波变换原理将网络流量序列分解成高频部分和低频部分,在此基础上对各个子序列分别建立相应的GARCH模型并进行预测;然后,使用小波变换原理将各个子序列的预测结果进行重构,从而最终实现对原始网络流量的预测。通过仿真实验表明,该模型的预测精度较之传统的小波变换与ARMA组合模型的预测精度得到了大幅提升。     

Heavy-tailed mixture GARCH volatility modeling and Value-at-Risk estimation

This paper presents a heavy-tailed mixture model for describing time-varying conditional distributions in time series of returns on prices. Student-t component distributions are taken to capture the heavy tails typically encountered in such financial data. We design a mixture MT(m)-GARCH(p, q) volatility model for returns, and develop an EM algorithm for maximum likelihood estimation of its parameters. This includes formulation of proper temporal derivatives for the volatility parameters. The experiments with a low order MT(2)-GARCH(1, 1) show that it yields results with improved statistical characteristics and economic performance compared to linear and nonlinear heavy-tail GARCH, as well as normal mixture GARCH. We demonstrate that our model leads to reliable Value-at-Risk performance in short and long trading positions across different confidence levels.     

Forecasting financial time series volatility using Particle Swarm Optimization trained Quantile Regression Neural Network

Accurate forecasting of volatility from financial time series is paramount in financial decision making. This paper presents a novel, Particle Swarm Optimization (PSO)-trained Quantile Regression Neural Network namely PSOQRNN, to forecast volatility from financial time series. We compared the effectiveness of PSOQRNN with that of the traditional volatility forecasting models, i.e., Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and three Artificial Neural Networks (ANNs) including Multi-Layer Perceptron (MLP), General Regression Neural Network (GRNN), Group Method of Data Handling (GMDH), Random Forest (RF) and two Quantile Regression (QR)-based hybrids including Quantile Regression Neural Network (QRNN) and Quantile Regression Random Forest (QRRF). The results indicate that the proposed PSOQRNN outperformed these models in terms of Mean Squared Error (MSE), on a majority of the eight financial time series including exchange rates of USD versus JPY, GBP, EUR and INR, Gold Price, Crude Oil Price, Standard and Poor 500 (S&P 500) Stock Index and NSE India Stock Index considered here. It was corroborated by the Diebold–Mariano test of statistical significance. It also performed well in terms of other important measures such as Directional Change Statistic (Dstat) and Theil's Inequality Coefficient. The superior performance of PSOQRNN can be attributed to the role played by PSO in obtaining the better solutions. Therefore, we conclude that the proposed PSOQRNN can be used as a viable alternative in forecasting volatility.     

一种自组织混合模型在汇率波动性预测中的应用

汇率波动性的预测一直以来是研究金融市场者关注的焦点之一,本文拓展了一种基于自组织神经网络技术的,用于预测非平稳汇率波动性的自组织混合模型(SOMAR).SOMAR突破了传统模型对平稳性的假设,变全局建模为局部建模,使得全局非平稳数据变成局部平稳数据.同时,它也是一种基于神经元网络技术的非参数回归模型,结合传统回归模型的简易性和神经元网络算法的灵活性,拓展模型(ESOMAR)提高了对数据异构的适应性.在对汇率波动性的预测实验中,ESOMAR体现出优于传统回归模型和一些基于其它神经元网络模型的效果,并证明了它在预测金融数据方面所具有的价值.     

Volatility Trading ia Temporal Pattern Recognition in Quantised Financial Time Series

We investigate the potential of the analysis of noisy non-stationary time series by quantising it into streams of discrete symbols and applying finite-memory symbolic predictors. Careful quantisation can reduce the noise in the time series to make model estimation more amenable. We apply the quantisation strategy in a realistic setting involving financial forecasting and trading. In particular, using historical data, we simulate the trading of straddles on the financial indexes DAX and FTSE 100 on a daily basis, based on predictions of the daily volatility differences in the underlying indexes. We propose a parametric, data-driven quantisation scheme which transforms temporal patterns in the series of daily volatility changes into grammatical and statistical patterns in the corresponding symbolic streams. As symbolic predictors operating on the quantised streams, we use the classical fixed-order Markov models, variable memory length Markov models and a novel variation of fractal-based predictors, introduced in its original form in Tin_ o and Dorffner [1]. The fractal-based predictors are designed to efficiently use deep memory. We compare the symbolic models with continuous techniques such as time-delay neural networks with continuous and categorical outputs, and GARCH models. Our experiments strongly suggest that the robust information reduction achieved by quantising the real-valued time series is highly beneficial. To deal with non-stationarity in financial daily time series, we propose two techniques that combine ‘sophisticated’ models fitted on the training data with a fixed set of simple-minded symbolic predictors not using older (and potentially misleading) data in the training set. Experimental results show that by quantising the volatility differences and then using symbolic predictive models, market makers can sometimes generate a statistically significant excess profit. We also mention some interesting observations regarding the memory structure in the series of daily volatility differences studied.     

A hybrid modeling approach for forecasting the volatility of S&P 500 index return

Forecasting volatility is an essential step in many financial decision makings. GARCH family of models has been extensively used in finance and economics, particularly for estimating volatility. The motivation of this study is to enhance the ability of GARCH models in forecasting the return volatility. We propose two hybrid models based on EGARCH and Artificial Neural Networks to forecast the volatility of S&P 500 index. The estimates of volatility obtained by an EGARCH model are fed forward to a Neural Network. The input to the first hybrid model is complemented by historical values of other explanatory variables. The second hybrid model takes as inputs both series of the simulated data and explanatory variables. The forecasts obtained by each of those hybrid models have been compared with those of EGARCH model in terms of closeness to the realized volatility. The computational results demonstrate that the second hybrid model provides better volatility forecasts.     

基于GARCH模型的网络新闻与舆情的波动性分析

网络新闻产生的舆情波动一般具有异方差特征,难以用普通模型拟合。由诺贝尔经济学奖获得者恩格尔教授提出的条件异方差(GARCH)模型在分析证券价格波动性方面获得极大成功。本文利用GARCH模型分析网络新闻与舆情的波动性,通过典型事件的舆情采集,分析数据的特征。研究表明,网络新闻与舆情的波动性符合GARCH模型的特征,通过参数的调整和检验,可以实现模型与数据的良好拟合。     

An algorithm for nonparametric GARCH modelling

A simple iterative algorithm for nonparametric first-order GARCH modelling is proposed. This method offers an alternative to fitting one of the many different parametric GARCH specifications that have been proposed in the literature. A theoretical justification for the algorithm is provided and examples of its application to simulated data from various stationary processes showing stochastic volatility, as well as empirical financial return data, are given. The nonparametric procedure is found to often give better estimates of the unobserved latent volatility process than parametric modelling with the standard GARCH(1,1) model, particularly in the presence of asymmetry and other departures from the standard GARCH specification. Extensions of the basic iterative idea to more complex time series models combining ARMA or GARCH features of possibly higher order are suggested.     

Fat tails and asymmetry in financial volatility models

Although the generalised autoregressive conditional heteroskedasticity (GARCH) model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student’s t-distribution performs best in capturing the non-normal aspects of the data.     

Applications of AR*-GRNN model for financial time series forecasting

AR* models contain Autoregressive Moving Average and Generalized Autoregressive Conditional Heteroscedastic class model which are widely used in time series. Recent researches in forecasting with Generalized Regression Neural Network (GRNN) suggest that GRNN can be a promising alternative to the linear and nonlinear time series models. In this paper, a model composed of AR* and GRNN is proposed to take advantage of their feathers in linear and nonlinear modeling. In the AR*-GRNN model, AR* modeling improves the forecasting performance of the combined model by capturing statistical and volatility information from the time series. The relative experiments testify that the combined model provides an effective way to improve forecasting performance which can be achieved by either of the models used separately.     

Modeling Hong Kong’s stock index with the Student t-mixture autoregressive model

It is well known that financial returns are usually not normally distributed, but rather exhibit excess kurtosis. This implies that there is greater probability mass at the tails of the marginal or conditional distribution. Mixture-type time series models are potentially useful for modeling financial returns. However, most of these models make the assumption that the return series in each component is conditionally Gaussian, which may result in underestimates of the occurrence of extreme financial events, such as market crashes. In this paper, we apply the class of Student t-mixture autoregressive (TMAR) models to the return series of the Hong Kong Hang Seng Index. A TMAR model consists of a mixture of g autoregressive components with Student t-error distributions. Several interesting properties make the TMAR process a promising candidate for financial time series modeling. These models are able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time-varied from short- to long-tailed or from unimodal to multi-modal. The use of Student t-distributed errors in each component of the model allows for conditional leptokurtic distribution, which can account for the commonly observed unconditional kurtosis in financial data.     

Sea surface target detection based on complex ARMA-GARCH processes

In financial applications, it is common practice to fit return series by AutoRegressive Moving-Average (ARMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. In this paper, we develop a complex-valued ARMA-GARCH model for the sea clutter modeling application. Compared with the AR-GARCH model, the additionally introduced MA terms make the proposed model capable of considering the dependence of conditional variances of adjacent echo measurements as model coefficients, improving the modeling precision by taking advantage of the strong correlations between adjacent measurements. Based on the complex-valued ARMA-GARCH process for sea clutter modeling, we further develop a sea surface target detection algorithm. By analyzing a large number of the practical sea clutter data, we evaluate its performance and show that the proposed sea surface target detector offers a noticeable improvement for the probability of detection, comparing with the state-of-the-art AR-GARCH detector.     

Volatility forecast using hybrid Neural Network models

In this research the testing of a hybrid Neural Networks-GARCH model for volatility forecast is performed in three Latin-American stock exchange indexes from Brazil, Chile and Mexico. A detail of the methodology and application of the volatility forecast of financial series using a hybrid artificial Neural Network model are presented.The results demonstrate that the ANN models can improve the forecasting performance of the GARCH models when studied in the three Latin-American markets and it is shown that the results are robust and consistent for different ANN specifications and different volatility measures.     

Bayesian estimation of the Gaussian mixture GARCH model

Bayesian inference and prediction for a generalized autoregressive conditional heteroskedastic (GARCH) model where the innovations are assumed to follow a mixture of two Gaussian distributions is performed. The mixture GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. Bayesian prediction of the Value at Risk is also addressed providing point estimates and predictive intervals. The method is illustrated using the Swiss Market Index.     

Improving prediction of exchange rates using Differential EMD

Volatility is a key parameter when measuring the size of errors made in modelling returns and other financial variables such as exchanged rates. The autoregressive moving-average (ARMA) model is a linear process in time series; whilst in the nonlinear system, the generalised autoregressive conditional heteroskedasticity (GARCH) and Markov switching GARCH (MS-GARCH) have been widely applied. In statistical learning theory, support vector regression (SVR) plays an important role in predicting nonlinear and nonstationary time series variables. In this paper, we propose a new algorithm, differential Empirical Mode Decomposition (EMD) for improving prediction of exchange rates under support vector regression (SVR). The new algorithm of Differential EMD has the capability of smoothing and reducing the noise, whereas the SVR model with the filtered dataset improves predicting the exchange rates. Simulations results consisting of the Differential EMD and SVR model show that our model outperforms simulations by a state-of-the-art MS-GARCH and Markov switching regression (MSR) models.     

基于高维状态空间方法构建金融市场网络模型

针对金融市场的核心变量--收益率和波动率，基于高维状态空间模型，利用EM和稀疏算法，分别建立了金融产品之间的收益率网络和波动率网络。前者刻画了金融产品收益之间的相互关系，后者刻画了金融产品风险之间的关系。相对于已有模型，上述模型可有效处理高维时间序列数据。对深圳、上海、香港和纽约市场的股票交易数据分析，找出了相应网络结构特征。以上市场的数据分析结果表明，相对于波动率网络，收益率网络具有更高的度数中心势，把这种现象归因于政策等因素对收益率的影响更为直接和简单，而对波动率的影响则是间接和复杂的。上述研究结果也为构建多变量波动率模型提供参考。     

Volatility Modeling by Asymmetrical Quadratic Effect with Diminishing Marginal Impact

This study presents evidence of an asymmetrical quadratic effect from financial asset return on volatility. The relationships between the two variables are quadratic for both positive and negative returns and systematically different in the two regimes. The convex relations are observed showing that extreme shocks have a diminishing marginal impact on volatility. A threshold quadratic model under GARCH framework is developed to capture the effect and applied to major stock indices. The empirical outcomes of quadratic regressions and in-sample estimations significantly confirm the asymmetrical quadratic behavior. With application of S&P500 series, both diagnoses of in-sample estimations and evaluations of out-of-sample forecasts verify the proposed specification as a valid alternative volatility modeling.     

A Student-<Emphasis Type="Italic">t</Emphasis> Full Factor Multivariate GARCH Model

We extend the full-factor multivariate GARCH model of Vrontos et al. (Econom J 6:312–334, 2003a) to account for fat tails in the conditional distribution of financial returns, using a multivariate Student-t error distribution. For the new class of Student-t full factor multivariate GARCH models, we derive analytical expressions for the score, the Hessian matrix and the Information matrix. These expressions can be used within classical inferential procedures in order to obtain maximum likelihood estimates for the model parameters. This fact, combined with the parsimonious parameterization of the covariance matrix under the full factor multivariate GARCH models, enables us to apply the models in high dimensional problems. We provide implementation details and illustrations using financial time series on eight stocks of the US market.     

A Hybrid Metaheuristic for the Efficient Solution of GARCH with Trend Models

GARCH with trend models represent an efficient tool for the analysis of different commodities via testing for a linear trend in the volatilities. However, to obtain the volatility of a given time series an instance from a particular class of scalar optimization problems (SOPs) has to be solved which still represents a challenge for existing solvers. We propose here a novel algorithm for the efficient numerical solution of such global optimization problems. The algorithm, DE–N, is a hybrid of Differential Evolution and the Newton method. The latter is widely used for the treatment of GARCH related models, but cannot be used as standalone algorithm in this case as the SOPs contain many local minima. The algorithm is tested and compared to some state-of-the-art methods on a benchmark suite consisting of 42 monthtly agricultural commodities series of the Mexican Consumer Price Index basket as well as on two series related to international prices. The results indicate that DE–N is highly competitive and that it is able to reliably solve SOPs derived from GARCH with trend models.