Volatility model selection for extremes of financial time series

Although both widely used in the financial industry, there is quite often very little justification why GARCH or stochastic volatility is preferred over the other in practice. Most of the relevant literature focuses on the comparison of the fit of various volatility models to a particular data set, which sometimes may be inconclusive due to the statistical similarities of both processes. With an ever growing interest among the financial industry in the risk of extreme price movements, it is natural to consider the selection between both models from an extreme value perspective. By studying the dependence structure of the extreme values of a given series, we are able to clearly distinguish GARCH and stochastic volatility models and to test statistically which one better captures the observed tail behaviour. We illustrate the performance of the method using some stock market returns and find that different volatility models may give a better fit to the upper or lower tails.     

Combining estimating functions for volatility

Accurate estimates of volatility are needed in risk management. Generalized autoregressive conditional heteroscedastic (GARCH) models and random coefficient autoregressive (RCA) models have been used for volatility modelling. Following Heyde [1997. Quasi-likelihood and its Applications. Springer, New York], volatility estimates are obtained by combining two different estimating functions. It turns out that the combined estimating function for the parameter in autoregressive processes with GARCH errors and RCA models contains maximum information. The combination of the least squares (LS) estimating function and the least absolute deviation (LAD) estimating function with application to GARCH model error identification is discussed as an application.     

An alternative method for forecasting price volatility by combining models

In this article, we study the volatility in the monthly price series of edible oils in domestic and international markets using the two popular family of nonlinear time-series models, viz, Generalized autoregressive conditional heteroscedastic (GARCH) models and Stochastic volatility (SV) models. To improve the forecasts of the volatility process, we also propose a new method of combining the volatility of these two competing models using the powerful technique of Kalman filter. The individual models as well as the combined models are assessed on their ability to predict the correct directional change (CDC) in future values as well as other goodness-of-fit statistics. Further, forecasting performance are also evaluated by computing various measures to validate the proposed methodology.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.     

ASSESSING AND TESTING FOR THRESHOLD NONLINEARITY IN STOCK RETURNS

This paper proposes a test for threshold nonlinearity in a time series with generalized autore‐gressive conditional heteroscedasticity (GARCH) volatility dynamics. This test is used to examine whether financial returns on market indices exhibit asymmetric mean and volatility around a threshold value, using a double‐threshold GARCH model. The test adopts the reversible‐jump Markov chain Monte Carlo idea of Green, proposed in 1995, to calculate the posterior probabilities for a conventional GARCH model and a double‐threshold GARCH model. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity with asymmetric behaviour of the mean and volatility. Simulation experiments demonstrate that the test works very well in distinguishing between the conventional GARCH and the double‐threshold GARCH models. In an application to eight international financial market indices, including the G‐7 countries, clear evidence supporting the hypothesis of threshold nonlinearity is discovered, simultaneously indicating an uneven mean‐reverting pattern and volatility asymmetry around a threshold return value.     

Wavelet Improvement of the Over-Rejection of Unit Root Test Under GARCH Errors: An Application to Swedish Immigration Data

In this article, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey–Fuller tests for unit root when the data is associated with volatility like the GARCH(1, 1) effect. The logic of this technique is based on the idea that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of the test in the wavelet environment is still the same as the traditional Dickey–Fuller type of tests. The finite sample property is improved when the data suffers from GARCH error. The investigation of the size property and the finite sample distribution of the test is carried out by Monte Carlo experiment. An empirical example with data on the net immigration to Sweden during the period 1950–2000 is used to illustrate the performance of the wavelet improved test under GARCH errors. The results reveal that using the traditional Dickey–Fuller type of tests, the unit root hypothesis is rejected while our wavelet improved test do not reject as it is more robust to GARCH errors in finite samples.     

非线性GARCH族的模型平均估计方法

本文考虑了非线性GARCH族的模型平均估计方法。在备选模型集合包含拥有不同模型结构的非线性GARCH族的情况下,本文构建了非线性GARCH族的模型平均估计量,并给出相应的权重选择准则。在一定正则条件下,本文证明上述模型平均估计量具有渐近最优性,即渐近实现真实最优的KL偏离度。蒙特卡洛模拟结果表明,在大部分情形下,本文提出的模型平均估计量取得了更小的相对KL偏离值。作为非线性GARCH族的模型平均估计方法的应用,本文对2016年6月1日至2017年6月1日上证指数的日波动率进行估计,与现有模型选择与模型平均方法相比较,本文模型平均估计方法具有更高的精度。     

Markov switching component GARCH model: Stability and forecasting

ABSTRACT

This paper introduces an extension of the Markov switching GARCH model where the volatility in each state is a convex combination of two different GARCH components with time varying weights. This model has the dynamic behavior to capture the variants of shocks. The asymptotic behavior of the second moment is investigated and an appropriate upper bound for it is evaluated. Using the Bayesian method via Gibbs sampling algorithm, a dynamic method for the estimation of the parameters is proposed. Finally, we illustrate the efficiency of the model by simulation and also by considering two different set of empirical financial data. We show that this model provides much better forecasts of the volatility than the Markov switching GARCH model.     

A robust closed-form estimator for the GARCH(1,1) model

In this paper we extend the closed-form estimator for the generalized autoregressive conditional heteroscedastic (GARCH(1,1)) proposed by Kristensen and Linton [A closed-form estimator for the GARCH(1,1) model. Econom Theory. 2006;22:323–337] to deal with additive outliers. It has the advantage that is per se more robust that the maximum likelihood estimator (ML) often used to estimate this model, it is easy to implement and does not require the use of any numerical optimization procedure. The robustification of the closed-form estimator is done by replacing the sample autocorrelations by a robust estimator of these correlations and by estimating the volatility using robust filters. The performance of our proposal in estimating the parameters and the volatility of the GARCH(1,1) model is compared with the proposals existing in the literature via intensive Monte Carlo experiments and the results of these experiments show that our proposal outperforms the ML and quasi-maximum likelihood estimators-based procedures. Finally, we fit the robust closed-form estimator and the benchmarks to one series of financial returns and analyse their performances in estimating and forecasting the volatility and the value-at-risk.     

Generalized EGARCH Random Effect Models Application to Financial Time Series

In this article, we propose a simple alternative model to analyze the volatility of the financial time series. In the applications, the performance of this model is compared with the performance of the GARCH type models. Using GARCH, EGARCH, and the proposed models, we analyze the time series of the Bovespa and Dow Jones Industrial Average indexes. In the applications we can see that the proposed models have good performance compared with the usual GARCH type model.     

Markov switch smooth transition HYGARCH model: Stability and estimation

Abstract

HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides a flexible structure to capture different levels of volatilities and also short and long memory effects. The necessary and sufficient condition for the asymptotic stability is derived. Forecast of conditional variance is studied by using all past information through a parsimonious way. Bayesian estimations based on Gibbs sampling are provided. A simulation study has been given to evaluate the estimations and model stability. The competitive performance of the proposed model is shown by comparing it with the HYGARCH and smooth-transition HYGARCH models for some period of the S&P500 and Dow Jones industrial average indices based on volatility and value-at-risk forecasts.     

波动率的持续性：基于GARCH模型的成交量解释

文章将成交量变量合理地分解为由好、坏消息分别引致的两部分,结合GARCH模型,研究了成交量对波动率持续性的解释,并得出如下结论:成交量变量对波动率的持续性具有一定的解释力;信息对波动率的影响具有不对称性,坏消息比好消息的影响大;将成交量分解成由好、坏消息分别引致的两部分之后,能够更进一步地解释波动率的持续性。     

Deciding between GARCH and stochastic volatility via strong decision rules

The GARCH and stochastic volatility (SV) models are two competing, well-known and often used models to explain the volatility of financial series. In this paper, we consider a closed form estimator for a stochastic volatility model and derive its asymptotic properties. We confirm our theoretical results by a simulation study. In addition, we propose a set of simple, strongly consistent decision rules to compare the ability of the GARCH and the SV model to fit the characteristic features observed in high frequency financial data such as high kurtosis and slowly decaying autocorrelation function of the squared observations. These rules are based on a number of moment conditions that is allowed to increase with sample size. We show that our selection procedure leads to choosing the model that fits best, or the simplest model under equivalence, with probability one as the sample size increases. The finite sample size behavior of our procedure is analyzed via simulations. Finally, we provide an application to stocks in the Dow Jones industrial average index.     

Indirect estimation of randomized generalized autoregressive conditional heteroskedastic models

The class of generalized autoregressive conditional heteroskedastic (GARCH) models can be used to describe the volatility with less parameters than autoregressive conditional heteroskedastic (ARCH)-type models, their distributions are heavy-tailed, with time-dependent conditional variance, and are able to model clustering of volatility. Despite all these facts, the way that GARCH models are built imposes limits on the heaviness of the tails of their unconditional distribution. The class of randomized generalized autoregressive conditional heteroskedastic (R-GARCH) models includes the ARCH and GARCH models allowing the use of stable innovations. Estimation methods and empirical analysis of R-GARCH models are the focus of this work. We present the indirect inference method to estimate the R-GARCH models, some simulations and an empirical application.     

A Stochastic Volatility Model With Conditional Skewness

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.     

Comparison of the finite mixture of ARMA-GARCH,back propagation neural networks and support-vector machines in forecasting financial returns

The use of GARCH type models and computational-intelligence-based techniques for forecasting financial time series has been proved extremely successful in recent times. In this article, we apply the finite mixture of ARMA-GARCH model instead of AR or ARMA models to compare with the standard BP and SVM in forecasting financial time series (daily stock market index returns and exchange rate returns). We do not apply the pure GARCH model as the finite mixture of the ARMA-GARCH model outperforms the pure GARCH model. These models are evaluated on five performance metrics or criteria. Our experiment shows that the SVM model outperforms both the finite mixture of ARMA-GARCH and BP models in deviation performance criteria. In direction performance criteria, the finite mixture of ARMA-GARCH model performs better. The memory property of these forecasting techniques is also examined using the behavior of forecasted values vis-à-vis the original values. Only the SVM model shows long memory property in forecasting financial returns.     

基于混频已实现GARCH模型的波动预测与VaR度量

本文将Hansen等（2012）的Realized GARCH模型扩展为包含日内收益率、日收益率以及已实现波动率的混频已实现GARCH模型（M-Realized GARCH模型）。该模型将日内交易分为前后两段,引入了混频均值方程,并对混频均值方程的残差分别建立条件波动率方程和已实现日波动率方程。本文采用2013-2016年沪深300指数混频数据,分别在扰动项服从正态分布、t分布和广义误差分布的假设下,采用损失函数、SPA检验、kupiec检验和动态分位数检验法,对GARCH、Realized GARCH和M-Realized GARCH模型的波动率预测和VaR度量效果对比研究,得出M-Realized GARCH模型能提高预测精度,且VaR实际失败率与理论失败率一致,失败发生之间不相关。最后,本文利用Block bootstrap方法抽样得到混频数据,模拟证明了M-Realized GARCH模型比Realized GARCH模型具有更高的预测精度。     

Performance of information criteria for spatial models

Model choice is one of the most crucial aspect in any statistical data analysis. It is well known that most models are just an approximation to the true data-generating process but among such model approximations, it is our goal to select the ‘best’ one. Researchers typically consider a finite number of plausible models in statistical applications, and the related statistical inference depends on the chosen model. Hence, model comparison is required to identify the ‘best’ model among several such candidate models. This article considers the problem of model selection for spatial data. The issue of model selection for spatial models has been addressed in the literature by the use of traditional information criteria-based methods, even though such criteria have been developed based on the assumption of independent observations. We evaluate the performance of some of the popular model selection critera via Monte Carlo simulation experiments using small to moderate samples. In particular, we compare the performance of some of the most popular information criteria such as Akaike information criterion (AIC), Bayesian information criterion, and corrected AIC in selecting the true model. The ability of these criteria to select the correct model is evaluated under several scenarios. This comparison is made using various spatial covariance models ranging from stationary isotropic to nonstationary models.     

房地产股票市场溢出效应研究

本文应用单变量GARCH模型和互相关函数探讨了不同市场之间的收益和波动的溢出效应;仿照收益的概念提出了“波动演进”,并使用向量自回归模型研究了波动和收益溢出的动态过程。研究发现,收益和波动的溢出存在地域特性,即同一地域的国家或地区之间存在快速且强烈的溢出效应。研究还揭示了一些国家或地区金融市场的特点,比如中国大陆是一个波动接受国,而德国是一个纯波动出口国。此外,通过比较平静时期和紧张时期的股市,可以观察到投资者的行为产生了变化,但是他们对信息的判断能力和速度并没有提高。     

Likelihood-Based comparison of stable paretian and competing models: Evidence from daily exchange rates

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major currencies. Inference is based on combining Monte Carlo methods with Laplace integration. The empirical results show that neither GARCH nor stable models are clear winners, and a GARCH model with stable innovations is the model best supported by the data.