Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non‐stationary Volatility

In this paper, we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to non‐stationary volatility. Extant estimators of the trend coefficient are analysed. We find that under heteroskedasticity, the Cochrane–Orcutt‐type estimator (with some initial condition) could be less efficient than Ordinary Least Squares (OLS) when the process is highly persistent, whereas it is asymptotically equivalent to OLS when the process is less persistent. An efficient non‐parametrically weighted Cochrane–Orcutt‐type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non‐stationary volatility of unknown form. The feasible estimator relies on non‐parametric estimation of the volatility function, and the asymptotic theory is provided. We use the data‐dependent smoothing bandwidth that can automatically adjust for the strength of non‐stationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of non‐stationary volatility. Finite‐sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators.     

LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS

Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared, and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In United States stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.     

Refined Inference on Long Memory in Realized Volatility

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et al., 2001; Martens et al., 2004). The present article provides some illustrative analysis of how long memory may arise from the accumulative process underlying realized volatility. The article also uses results in Lieberman and Phillips (2004, 2005) to refine statistical inference about d by higher order theory. Standard asymptotic theory has an O(n^-1/2) error rate for error rejection probabilities, and the theory used here refines the approximation to an error rate of o(n^-1/2). The new formula is independent of unknown parameters, is simple to calculate and user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et al. (2001) and Martens et al. (2004) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory, and generally confirms earlier findings.     

HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIES

To capture mean and variance asymmetries and time‐varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy‐tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time‐delay parameter. Self‐exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value‐at‐risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models.     

上海股票市场波动实证性研究:2001--从交易方式角度透视

我国股票市场上的交易方式有两种,即集合竞价和连续竞价,交易方式的差异会对股价的波动性产生影响,而市场的波动性对股票市场而言是双刃剑,因此从交易方式角度探求股市的适度波动成为理论工作的一个重心.本文以上海股票市场为研究对象,针对2001年的全部交易数据进行实证研究.结果表明,集合竞价形成的开盘价格收益率的方差大于连续竞价形成的收盘价格收益率的方差,其原因在于集合竞价与连续竞价相比,其交易过程的透明度差和交易指令具有不可更改性,据此,从交易制度上提出政策建议.     

Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory

Nonlinear functions of multivariate financial time series can exhibit long memory and fractional cointegration. However, tools for analysing these phenomena have principally been justified under assumptions that are invalid in this setting. Determination of asymptotic theory under more plausible assumptions can be complicated and lengthy. We discuss these issues and present a Monte Carlo study, showing that asymptotic theory should not necessarily be expected to provide a good approximation to finite-sample behavior.     

Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

ABSTRACT.  This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non-compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.     

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。     

股市联动中的“涟漪效应”

本文提出"涟漪效应"来解释国际股市联动性的大幅波动。所谓涟漪效应就是中心市场特有波动对其它市场间联动性产生影响的现象。本文采用滚动窗口和DCC-GARCH的方法计算了市场特有波动和收益相关系数,以9个主要市场指数为样本对国际股票市场中涟漪效应进行实证检验。研究结果显示,2007年后国际股市联动性变化与美国市场的涟漪效应有关,美国市场特有波动升高（降低）会导致全球股市联动性升高（降低）,而其他市场特有波动并没有类似影响。美国市场与其他市场间联动性基本不受第三方市场特有波动的影响,A股与美股联动性的增强是造成A股与其它股市联动性变化的主要原因。此外,研究特有波动与相关系数的关系能帮助我们识别国际股市中风险传递方向,本文结果显示欧洲市场对其他市场的影响非常有限,以往研究可能高估了欧洲市场的影响力。本文丰富了股市联动性影响因素的研究,对理解市场联动性变化、评估市场影响力等问题有重要意义。     

金融市场多标度分形现象及与风险管理的关系

已有研究通过对汇率、股票收益率、黄金价格等金融市场实证数据的分析,发现这些数据 具有多标度分形(multifractal) 特征. 通过对中国金融市场的代表数据之一———上海证券交易 所综合股价指数(SSECI) 的研究得出了相似的结论,并且初步提出了运用多标度分形理论所 提供的信息来进行金融风险管理的风险管理思路.