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U. S. National Income Series Revised—Congress Votes No on Censuses of Business and Manufactures—Britain Revises Living Cost Index-U. S. and U. K. Surveys Uncover Lacks in Statistical Training-Forthcoming Statistical Conferences     

Lag Length Selection in DF-GLS Unit Root Tests

We reinvestigate the empirical problem of lag length selection in unit root tests when using the augmented Dickey–Fuller test based on GLS-detrending. We extend the Ng and Perron (1995 Ng , S. , Perron , P. ( 1995 ). Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag . Journal of American Statistical Association 90 : 268 – 281 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) work on this issue by applying the finite sample critical values calculated using the formulae proposed by Cheung and Lai (1995 Cheung , Y. W. , Lai , K. S. ( 1995 ). Lag order and critical values of a modified Dickey–Fuller test . Oxford Bulletin of Business and Economics 57 : 411 – 418 .[Crossref] , [Google Scholar]). Unlike Ng and Perron (2001 Ng , S. , Perron , P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554.[Crossref], [Web of Science ®] , [Google Scholar]) we find through simulation studies that the method of selecting lag length using the sequential t-test in the ADF regression of GLS-detrended series performs the best in most cases.     

A Bias–Reduced Log–Periodogram Regression Estimator for the Long–Memory Parameter

In this paper, we propose a simple bias–reduced log–periodogram regression estimator, ^d_r, of the long–memory parameter, d, that eliminates the first– and higher–order biases of the Geweke and Porter–Hudak (1983) (GPH) estimator. The bias–reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2k for k=1,…,r, for some positive integer r, as additional regressors in the pseudo–regression model that yields the GPH estimator. The reduction in bias is obtained using assumptions on the spectrum only in a neighborhood of the zero frequency. Following the work of Robinson (1995b) and Hurvich, Deo, and Brodsky (1998), we establish the asymptotic bias, variance, and mean–squared error (MSE) of ^d_r, determine the asymptotic MSE optimal choice of the number of frequencies, m, to include in the regression, and establish the asymptotic normality of ^d_r. These results show that the bias of ^d_r goes to zero at a faster rate than that of the GPH estimator when the normalized spectrum at zero is sufficiently smooth, but that its variance only is increased by a multiplicative constant. We show that the bias–reduced estimator ^d_r attains the optimal rate of convergence for a class of spectral densities that includes those that are smooth of order s≥1 at zero when r≥(s−2)/2 and m is chosen appropriately. For s>2, the GPH estimator does not attain this rate. The proof uses results of Giraitis, Robinson, and Samarov (1997). We specify a data–dependent plug–in method for selecting the number of frequencies m to minimize asymptotic MSE for a given value of r. Some Monte Carlo simulation results for stationary Gaussian ARFIMA (1, d, 1) and (2, d, 0) models show that the bias–reduced estimators perform well relative to the standard log–periodogram regression estimator.     

违约预测的小波结构模型研究

本文针对上市公司违约预测问题,按照行业类型对我国2009年的上市企业进行分层抽样,构建了小波结构模型.小波结构模型通过应用小波变换来分解上市公司日收益序列,进而对低频序列和高频序列分别构建预测模型,再依据预测模型对未来收益进行预测,最后使用小波逆变换重构预测收益序列.通过小波结构模型可以避免时间序列模型进行收益波动预测的累加计算过程.在结合我国上市公司的实际数据对这两种模型的校验中,可以发现小波结构模型比时序结构模型在违约预测上有更好的识别力和准确度.     

Dynamic Forecasting Conditional Probability of Bombing Attacks Based on Time‐Series and Intervention Analysis

In recent years, various types of terrorist attacks occurred, causing worldwide catastrophes. According to the Global Terrorism Database (GTD), among all attack tactics, bombing attacks happened most frequently, followed by armed assaults. In this article, a model for analyzing and forecasting the conditional probability of bombing attacks (CPBAs) based on time‐series methods is developed. In addition, intervention analysis is used to analyze the sudden increase in the time‐series process. The results show that the CPBA increased dramatically at the end of 2011. During that time, the CPBA increased by 16.0% in a two‐month period to reach the peak value, but still stays 9.0% greater than the predicted level after the temporary effect gradually decays. By contrast, no significant fluctuation can be found in the conditional probability process of armed assault. It can be inferred that some social unrest, such as America's troop withdrawal from Afghanistan and Iraq, could have led to the increase of the CPBA in Afghanistan, Iraq, and Pakistan. The integrated time‐series and intervention model is used to forecast the monthly CPBA in 2014 and through 2064. The average relative error compared with the real data in 2014 is 3.5%. The model is also applied to the total number of attacks recorded by the GTD between 2004 and 2014.     

函数级数一致收敛的一个充要条件

证明了函数级数一致收敛的一个充要条件 ,进一步讨论了函数级数一致收敛的本质特征     

无穷级数比值判别法的推广

给出了正项级数关于敛散性的一个新的判别法 ,这一方法推广了达朗贝尔比值判别法     

杨幺“陆耕水战”的战略战术

南宋洞庭湖区杨幺农民起义能够6次击败朝廷官军围剿，坚持斗争达7年之久，其根本的立足法宝，就在于“陆耕水战”的战略战术。这一战略战术之所以特具威力．一是与其深入进行各种反封建斗争密切相连，从而具有广泛的群众基础；二是他们创制了当时最先进的水战工具，并施以因地制宜、灵活机动的各种战术。这两个方面是过去研究者未能涉及和论述的。     

Carleman不等式的加强

利用幂级数相关理论和一些初等不等式,建立了 Carleman 不等式的一序列加强不等式。     

Extremes of Markov chains with tail switching potential

Summary.  A recent advance in the utility of extreme value techniques has been the characteri- zation of the extremal behaviour of Markov chains. This has enabled the application of extreme value models to series whose temporal dependence is Markovian, subject to a limitation that prevents switching between extremely high and extremely low levels. For many applications this is sufficient, but for others, most notably in the field of finance, it is common to find series in which successive values switch between high and low levels. We term such series Markov chains with tail switching potential, and the scope of this paper is to generalize the previous theory to enable the characterization of the extremal properties of series displaying this type of behaviour. In addition to theoretical developments, a modelling procedure is proposed. A simulation study is made to assess the utility of the model in inferring the extremal dependence structure of autoregressive conditional heteroscedastic processes, which fall within the tail switching Markov family, and generalized autoregressive conditional heteroscedastic processes which do not, being non-Markov in general. Finally, the procedure is applied to model extremal aspects of a financial index extracted from the New York Stock Exchange compendium.