日已实现波动的估计研究

0引言在随着计算机技术的飞速发展和数据记录存储技术的提高,随之而来的存储成本的降低使得更多的研究者能够使用这些更精细的时间刻度观测到的数据集,即所谓的高频数据并且使数据频率达到了更高的极限例如Tick—by—Tick或者被称为超高频数据(ultra—high一frequency)。从实践     

基于高频数据的沪指波动长记忆性驱动因素分析

借助于高频数据的最优取样法,利用已实现波动率给出的上证指数波动率的有效估计,在研究已实现波动率特性的基础上,用计量模型探讨沪指波动的长记忆特征.发现HAR-RV模型比FARIMA模型更能有效地刻画沪指波动的长记忆性,且HAR-RV模型样本外预测效果远远优于FARIMA模型,这说明沪指波动具有伪长记忆性,表面特征显示的长记忆性是由短期投资、中期投资和长期投资形成的短记忆性叠加而成.同时由于HAR-RV模型综合考虑了不同时间水平上的已实现波动率,从而在深层次上验证了中国股票市场的异质性和波动率的杠杆效应.     

已实现波动率在我国金融市场的应用前景

作为金融计量学研究的一种新工具,已实现波动率以它独特的优势赢得了学者们的青睐,溶入了金融计量学各个分支领域的研究,并在一定程度上推动着这些领域的发展.然而,这种新兴的方法也不可避免地存在一些问题,有待于未来研究工作的改进和拓展.在我国金融市场未来的发展中,已实现波动率将发挥不可低估的作用.     

ACD模型及其扩展--金融高频数据计量模型的新动态

本文结合高频数据所表现出的独有特征系统地回顾了近年ACD(Autoregressive Conditional Duration)模型及其扩展在国际、国内的发展状况,展望了该模型的发展方向.     

基于高频数据的金融波动率模型

金融高频数据和金融波动率是目前金融领域研究的热点问题。本文对基于金融高频数据的金融波动率估计量——已实现双幂次变差进行了建模和预测。已实现双幂次变差无模型、计算简便,在一定条件下是金融波动率的无偏估计量,并且具有稳健性和有效性。通过用上证综指对已实现双幂次变差进行ARFIMA建模,发现中国股票市场的上证综指已实现双幂次变差时间序列具有长记忆性。     

多维高频时间序列的波动持续性质研究

本文对多维高频金融时间序列的"已实现"协方差阵提出相应的模型并进行建模,在此基础上研究了波动持续性质;讨论了高频时间序列的协方差平稳性与波动持续性的关系,同时证明了基于高频数据的协同持续定义与Bollerslev和Engle提出的协同持续概念具有内在的一致性;扩展线性持续到非线性情况,讨论了它们之间的内在关系,指出了持续性质在动态组合投资、风险规避策略中的意义和作用.     

实现相关系数模型:基于动态相关高频Bi-GARCH过程的MC检验

使用高频数据构建的实现波动率已被多数文献证实具有良好的实证性质和应用前景。文章通过构建具有不同动态相关模式的高频Bi-GARCH模型,对其多元方向扩展的实现相关系数模型捕捉变动金融资产价格相关系数的能力和其他常用模型进行了蒙特卡洛对比测试。研究证明,该模型与其他模型相比是否具有显著优势依赖于相关系数的变化方式:当金融市场较为平稳,资产价格相关系数相对稳定时,此类方法并不明显的优于其它方法;然而当金融市场急剧变化导致资产价格相关系数快速变动时,此类方法要显著优于其它方法。     

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。     

期权定价中的波动率估计

本文旨在研究Black-Scholes期权定价模型中重要参数波动率的估计问题,了解波动率估计的简单易行的标准方法,介绍了历史波动率和隐含波动率的估计技术.     

基于金融高频数据的VaR研究

选取具有良好统计性质的金融波动率估计量来构建VaR,,可以使市场风险的度量更为准确.高频数据由于比低频数据包含了更多的市场信息,因此基于高频数据的金融波动率估计量更为准确.但是基于高频数据的波动率估计量为数众多,目前仅有对各个估计量本身性质的比较研究,在应用于VaR的研究中如何选取估计量使得VaR的计算更为准确则不得而知.因此,文章选取了高频数据下的若干个有代表性的金融波动率估计量,进行VaR值的计算,并对其结果进行了比较研究,同时进行了持续性分析.通过实证研究表明V2R序列具有持续性,其中由赋权"已实现"双幂次变差计算所得的VaR值更准确,从而为VaR的精确计算和正确建模提供了依据.     

Nonparametric Estimation Methods of Integrated Multivariate Volatilities

Estimation of integrated multivariate volatilities of an Itô process is an interesting and important issue in finance, for example, in order to evaluate portfolios. New non-parametric estimators have been recently proposed by Malliavin and Mancino (2002 Malliavin , P. , Mancino , M. ( 2002 ). Fourier series method for measurement of multivariate volatilities . Finance and Stochastics 6 : 49 – 61 .[Crossref], [Web of Science ®] , [Google Scholar]) and Hayashi and Yoshida (2005a Hayashi , T. , Yoshida , N. (2005a). On covariance estimation of nonsynchronously observed diffusion processes. Bernoulli 11(2):359–379.[Crossref], [Web of Science ®] , [Google Scholar]) as alternative methods to classical realized quadratic covariation. The purpose of this article is to compare these alternative estimators both theoretically and empirically, when high frequency data is available. We found that the Hayashi–Yoshida estimator performs the best among the alternatives in view of the bias and the MSE. The other estimators are shown to have possibly heavy bias mostly toward the origin. We also applied these estimators to Japanese Government Bond futures to obtain the results consistent with our simulation.     

Estimation of Periodic Bilinear Time Series Models

In this article, a new class of models is proposed for modeling nonlinear and nonstationary time series. This new class of models, referred to as the periodic bilinear models, has a state space representation and can be characterized by a set of recursive equations. Condition for the stationarity is presented. Procedures for parameter estimation using the cumulants of order less than four are described and the accuracy of the proposed method is demonstrated in the Monte Carlo simulations.     

Fitting Time Series Models by Minimizing Multistep-ahead Errors: a Frequency Domain Approach

This paper brings together two topics in the estimation of time series forecasting models: the use of the multistep-ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization. The methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients. This includes the IMA(1, 1) model for which the common exponentially weigh-ted moving average predictor is optimal, besides more general structural models for series exhibiting trends and seasonality. The method is extended to include the Box–Jenkins `air line' model. The value of the multistep criterion is that it provides protection against using an incorrectly specified model. The value of frequency domain estimation is that the iteratively reweighted least squares scheme for fitting generalized linear models is readily extended to construct the parameter estimates and their standard errors. It also yields insight into the loss of efficiency when the model is correct and the robustness of the criterion against an incorrect model. A simple example is used to illustrate the method, and a real example demonstrates the extension to seasonal models. The discussion considers a diagnostic test statistic for indicating an incorrect model.     

Estimation of Correlation for Continuous Semimartingales

Abstract. In this study we are concerned with inference on the correlation parameter ρ of two Brownian motions, when only high‐frequency observations from two one‐dimensional continuous Itô semimartingales, driven by these particular Brownian motions, are available. Estimators for ρ are constructed in two situations: either when both components are observed (at the same time), or when only one component is observed and the other one represents its volatility process and thus has to be estimated from the data as well. In the first case it is shown that our estimator has the same asymptotic behaviour as the standard one for i.i.d. normal observations, whereas a feasible estimator can still be defined in the second framework, but with a slower rate of convergence.     

Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models

An exact maximum likelihood method is developed for the estimation of parameters in a non-Gaussian nonlinear density function that depends on a latent Gaussian dynamic process with long-memory properties. Our method relies on the method of importance sampling and on a linear Gaussian approximating model from which the latent process can be simulated. Given the presence of a latent long-memory process, we require a modification of the importance sampling technique. In particular, the long-memory process needs to be approximated by a finite dynamic linear process. Two possible approximations are discussed and are compared with each other. We show that an autoregression obtained from minimizing mean squared prediction errors leads to an effective and feasible method. In our empirical study, we analyze ten daily log-return series from the S&P 500 stock index by univariate and multivariate long-memory stochastic volatility models. We compare the in-sample and out-of-sample performance of a number of models within the class of long-memory stochastic volatility models.     

Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach

Abstract.  We propose a global smoothing method based on polynomial splines for the estimation of functional coefficient regression models for non-linear time series. Consistency and rate of convergence results are given to support the proposed estimation method. Methods for automatic selection of the threshold variable and significant variables (or lags) are discussed. The estimated model is used to produce multi-step-ahead forecasts, including interval forecasts and density forecasts. The methodology is illustrated by simulations and two real data examples.     

基于图方法的MA和ARMA模型系数检验

应用图模型方法来讨论传统的MA和ARMA模型,证明了MA和ARMA模型的系数为去掉其他时间序列分量线性效应的条件下的偏相关系数,且利用图模型推断算法提出了一种新的参数估计和检验方法。     

Estimation of structural mean breaks for long-memory data sets

In long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.     

A Bayesian Approach for Nonlinear Regression Models with Continuous Errors

Abstract

In this paper we develop a Bayesian analysis for the nonlinear regression model with errors that follow a continuous autoregressive process. In this way, unequally spaced observations do not present a problem in the analysis. We employ the Gibbs sampler, (see Gelfand, A., Smith, A. (1990 Gelfand, A. and Smith, A. 1990. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc., 85: 398–409. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:398–409.), as the foundation for making Bayesian inferences. We illustrate these Bayesian inferences with an analysis of a real data-set. Using these same data, we contrast the Bayesian approach with a generalized least squares technique.     

Power Variations and Testing for Co‐Jumps: The Small Noise Approach

In this paper, we study the effects of noise on bipower variation, realized volatility (RV) and testing for co‐jumps in high‐frequency data under the small noise framework. We first establish asymptotic properties of bipower variation in this framework. In the presence of the small noise, RV is asymptotically biased, and the additional asymptotic conditional variance term appears in its limit distribution. We also propose consistent estimators for the asymptotic variances of RV. Second, we derive the asymptotic distribution of the test statistic proposed in (Ann. Stat. 37, 1792‐1838) under the presence of small noise for testing the presence of co‐jumps in a two‐dimensional Itô semimartingale. In contrast to the setting in (Ann. Stat. 37, 1792‐1838), we show that the additional asymptotic variance terms appear and propose consistent estimators for the asymptotic variances in order to make the test feasible. Simulation experiments show that our asymptotic results give reasonable approximations in the finite sample cases.