Mean–variance portfolio selection with ‘at-risk’ constraints and discrete distributions

We examine the impact of adding either a VaR or a CVaR constraint to the mean–variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K + 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K + 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean–variance model.     

Improved estimation of extreme quantiles in the multivariate Lomax (Pareto II) distribution

Estimation of a quantile of the common marginal distribution in a multivariate Lomax (Pareto II) distribution with unknown location and scale parameters is considered. For quadratic loss and specified extreme quantiles, it is established that the best affine equivariant procedure is inadmissible by constructing a better estimator.     

Forecast reconciliation: A geometric view with new insights on bias correction

A geometric interpretation is developed for so-called reconciliation methodologies used to forecast time series that adhere to known linear constraints. In particular, a general framework is established that nests many existing popular reconciliation methods within the class of projections. This interpretation facilitates the derivation of novel theoretical results. First, reconciliation via projection is guaranteed to improve forecast accuracy with respect to a class of loss functions based on a generalised distance metric. Second, the Minimum Trace (MinT) method minimises expected loss for this same class of loss functions. Third, the geometric interpretation provides a new proof that forecast reconciliation using projections results in unbiased forecasts, provided that the initial base forecasts are also unbiased. Approaches for dealing with biased base forecasts are proposed. An extensive empirical study of Australian tourism flows demonstrates the theoretical results of the paper and shows that bias correction prior to reconciliation outperforms alternatives that only bias-correct or only reconcile forecasts.     

The uncertainty track: Machine learning,statistical modeling,synthesis

This note provides an evaluation of the contributions of the M5 Competition to the construction of prediction intervals. We consider the choice of criteria used in the evaluations, the relative performance of designed and benchmark methods and the take-home lessons both for statistical forecasters and for those interested in forecasting retail sales.     

Statistical Scale Space Methods

The goal of statistical scale space analysis is to extract scale‐dependent features from noisy data. The data could be for example an observed time series or digital image in which case features in either different temporal or spatial scales would be sought. Since the 1990s, a number of statistical approaches to scale space analysis have been developed, most of them using smoothing to capture scales in the data, but other interpretations of scale have also been proposed. We review the various statistical scale space methods proposed and mention some of their applications.     

On Families of Distributions with Shape Parameters

Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi‐dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all‐important location and scale parameters. One important and useful family is comprised of the ‘skew‐symmetric’ distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call ‘transformation of scale’—including two‐piece distributions—and by probability integral transformation of non‐uniform random variables. I also treat briefly the issues of multi‐variate extension, of distributions on subsets of and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute     

用于APSK和QAM信号信噪比估计的改进分段数据拟合算法

为提高幅相键控(APSK)信号和正交调幅(QAM)信号信噪比估计范围和精度,提出了一种改进的信号信噪比估计算法。算法首先计算接收信号平方的均值和绝对值的均值之比,然后根据星座图特征,利用多项式拟合该比值与信噪比的关系。在拟合过程中,对信噪比区间进行分段拟合来提高各段拟合精度,并用蒙特卡洛仿真经验值修正算法的固有偏差,从而得到信噪比的近似无偏估计。仿真结果表明,当信噪比估计区间为-5~20 dB且数据长度合适时,16APSK和32APSK信号信噪比估计偏差均值小于0.5 dB,标准差小于2 dB;该算法对16QAM和32QAM信号信噪比估计的标准差小于传统数据拟合算法。该算法运算复杂度较低,便于实时应用和硬件实现,对恒模和非恒模信号均能实现信噪比宽范围精确盲估计。     

基于 Tweedie 类分布的广义可加模型在车险费率厘定中的应用

分析广义线性模型和广义可加模型的理论基础和特点,从Tweedie类分布的独特视角归纳保险索赔额数据的分布规律。基于此建立了GLM—Tweedie和GAM—Tweedie索赔额拟合模型,以一组汽车保险损失数据为样本进行车险费率厘定和索赔额拟合的实证分析,识别“车、人、地”不同因素对费率不同的影响程度,助推我国车险费率厘定市场化改革精算技术的提升。     

大城市客运交通系统出行方式特性分析

以我国大城市客运交通系统为研究对象,对各出行方式的出行距离与出行时耗分别进行了分布拟合。研究发现,采用k阶爱尔朗分布拟合表现出良好的适用性。在出行距离方面,小汽车与自行车的出行距离分布随机性最大,常规公交次之,城市轨道交通相对来说出行距离随机性最小;在出行时耗方面,自行车的时耗分布最为集中,小汽车与出租车次之,常规公交与城市轨道交通出行时耗分布范围最广。     

Bootstrapping Financial Time Series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.