The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Maximum likelihood estimation in a Weibull regression model with type-1 censoring: a Monte Carlo study

Results of the Monte Carlo study of the performance of a maximum likelihood estimation in a Weibull parametric regression model with two explanatory variables are presented. One simulation run contained 1000 samples censored on the average by the amount of 0-30%. Each simulatedsample was generated in a form of two-factor two-level balanced experiment. The confidence intervals were computed using the large-sample normal approximation via the matrix of observed information. For small sample sizes the estimates of the scale parameter b of the loglifetime were significantly negatively biased, which resulted in a poor quality of confidence intervals for b and the low-level quantiles. All estimators improved their quality when the nominal value of b decreased. A moderate amount of censoring improved the quality of point and confidence estimation. The reparametrization b 7 produced rather accurate confidence intervals. Exact confidence intervals for b in case of non-censoring were obtained using the pivotal quantity b/b.     

Tukey-Type Distributions in the Context of Financial Data

Abstract

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPI) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares “average” distributions obtained under the null and alternative models in the sense of Wald (1947 Wald , A. ( 1947 ). Sequential Analysis . New York : Wiley . [Google Scholar] 1950 Wald , A. ( 1950 ). Statistical Decision Functions . New York : Wiley . [Google Scholar]). In contrast, a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one-parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ.     

A Simpler Approximation for Areas under the Standard Normal Curve

A simple approximation for areas under the standard normal curve is presented that is suitable for use when tables and/or calculators are not available or not permitted.     

Online Control Charts for Process Averages Based on Repeated Median Filters

Two types of estimates of process level, namely repeated median estimates (Siegel, 1982 Siegel , A. F. ( 1982 ). Robust regression using repeated medians . Biometrika 69 : 242 – 244 .[Crossref], [Web of Science ®] , [Google Scholar]) and full online estimates (Gather et al., 2006 Gather , U. , Schettlinger , K. , Fried , R. ( 2006 ). Online signal extraction by robust linear regression . Computational Statistics 21 : 33 – 51 .[Crossref], [Web of Science ®] , [Google Scholar]) based on repeated median filters, are used to develop control charts. The distributional properties of the estimates are studied using simulation and these are found to closely follow normal distribution. The repeated median being robust against outliers with asymptotically 50% breakdown value and having small standard deviation is found to be useful as a basis for monitoring process averages. The control charts using repeated median estimates have been recommended for general use.     

近代巴蜀诗人李士棻生卒年及别号考略

近代巴蜀诗人李士棻曾被曾国藩誉为“太白醉魂”，为曾府门下“四川三李”之一，其诗作有浓郁的巴蜀文化特色。然李氏仕宦不显，长期以来学界对其关注不足，学界近年不多的相关研究，多围绕国内所存的文献，对其诗歌创作进行艺术分析，对诗人的生平介绍多简单略过，没有严谨的考证，目前仍然很有争议。通过搜罗国内外现存典籍，综合目前所见李士棻本人著述，辅以晚清近代重要报刊《申报》和与李氏有交往的朝鲜文人文献，考证其生卒年及别号，冀为今后的相关研究解决基础问题。     

Influence diagnostics for the structural sharpe model under normal/independent distributions

A method is proposed in this paper to assess the local influence of minor perturbations for the Sharpe model when the normal distribution is replaced by normal/independent (NI) distributions. The family of NI distributions is an attractive class of symmetric heavy-tailed densities that includes as special cases the normal, t-Student, slash, and the contaminated normal distributions. Since the returns of the market are not observable, the statistical analysis is carried out in the context of an errors-in-variables model. An influence analysis for detecting influential observations (atypical returns) is developed to investigate the sensitivity of the maximum likelihood estimators. Diagnostic measures are obtained based on the conditional expectation of the complete-data log-likelihood function. The results are illustrated by using a set of shares of companies traded in the Chilean stock market.     

新常态下交通对中国经济质量增长的贡献

根据交通外部性和非线性理论构建交通门槛模型,并基于1985-2012年中国省际面板数据,采用Hansen门槛效应的内生分组方法检验新常态下交通对中国经济增长质量的贡献。结果显示：新常态下交通对经济增长质量贡献略低于"旧常态",但仍表现出区间"递增"趋势;把新常态下TFP分解为技术进步和技术效率,发现中密度地区要素配置结构已不适应技术进步的需要,高密度地区技术效率相对技术进步对经济增长质量的贡献较低;随着区间交通密度的增加,"政府干预经济"更有效率,但城市化和产业发展对经济增长质量贡献由正转负。为进一步提升新常态下交通对中国经济增长质量的贡献,应定向适度加大"中密度地区"交通投资力度,助其跳出"低增长陷阱";借助信息化、智能化手段引领交通建设转型升级以提高经济运行效率;构建"交通-产业-城镇"三位一体的协同新型综合交通体系;协调好城市化与交通基础设施建设之间的关系。