Dynamic generalized extreme value modeling via particle filters

This article addresses how particle filters compare to MCMC methods for posterior density approximations of a model that allows for a dynamic state with fixed parameters and where the observation equation is nonlinear. This is a problem that was not been well studied in the specialized literature. We prove that these state and parameter estimations can be achieved via particle filter methods without the need of more expensive Forward Filtering Backward Sampling (FFBS) simulation. Estimation of a time-varying extreme value model via the generalized extreme value distribution is considered using these particle filter methods and compared to a MCMC algorithm that involves a variety of Metropolis-Hastings steps. We illustrate and compare the different methodologies with simulated data and some minimum daily stock returns occurring monthly from January 4, 1990 to December 28, 2007 using the Tokyo Stock Price Index (TOPIX).     

The impact of jumps and leverage in forecasting covolatility

ABSTRACT

The paper investigates the impact of jumps in forecasting covolatility, accommodating leverage effects. We modify the preaveraged truncated covariance estimator of Koike (2016 Koike, Y. (2016). Estimation of integrated covariances in the simultaneous presence of non-synchronicity, microstructure noise and jumps. Econometric Theory 32:533–611.[Crossref], [Web of Science ®] , [Google Scholar]) such that the estimated matrix is positive definite. Using this approach, we can disentangle the estimates of the integrated covolatility matrix and jump variations from the quadratic covariation matrix. Empirical results for three stocks traded on the New York Stock Exchange indicate that the cojumps of two assets have a significant impact on future covolatility, but the impact is negligible for forecasting weekly and monthly horizons.     

非对称随机波动模型在中国股市的应用

为了探测随机波动模型的非对称特征,修改传统的随机波动模型建立非对称的随机波动模型,采用基于马尔可夫链蒙特卡洛(MCMC)模拟的贝叶斯分析对模型进行参数估计。对中国深圳、上海股市波动进行实证研究发现,非对称随机波动模型能较好地探测波动存在的非对称波动。与GJR-GARCH模型相比,非对称随机波动模型预测效果更好。     

Bayesian dynamic models for survival data with a cure fraction

In this paper, we propose a new class of semi-parametric cure rate models. Specifically, we construct dynamic models for piecewise hazard functions over a finite partition of the time axis. Allowing the size of partition and the levels of baseline hazard to be random, our proposed models provide a great flexibility in controlling the degree of parametricity in the right tail of the survival distribution and the amount of correlations among the log-baseline hazard levels. Several properties of the proposed models are derived, and propriety of the implied posteriors with improper noninformative priors for regression coefficients based on the proposed models is established for the fixed partition of the time axis. In addition, an efficient reversible jump computational algorithm is developed for carrying out posterior computation. A real data set from a melanoma clinical trial is analyzed in detail to further demonstrate the proposed methodology.     

A distance-based diagnostic for trans-dimensional Markov chains

Over the last decade the use of trans-dimensional sampling algorithms has become endemic in the statistical literature. In spite of their application however, there are few reliable methods to assess whether the underlying Markov chains have reached their stationary distribution. In this article we present a distance-based method for the comparison of trans-dimensional Markov chain sample output for a broad class of models. This diagnostic will simultaneously assess deviations between and within chains. Illustration of the analysis of Markov chain sample-paths is presented in simulated examples and in two common modelling situations: a finite mixture analysis and a change-point problem.     

BAYESIAN ESTIMATION OF RUIN PROBABILITIES WITH A HETEROGENEOUS AND HEAVY-TAILED INSURANCE CLAIM-SIZE DISTRIBUTION

This paper describes a Bayesian approach to make inference for risk reserve processes with an unknown claim‐size distribution. A flexible model based on mixtures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes, such as long tails and heterogeneity. A Bayesian density estimation approach for the claim sizes is implemented using reversible jump Markov chain Monte Carlo methods. An advantage of the considered mixture model is that it belongs to the class of phase‐type distributions, and thus explicit evaluations of the ruin probabilities are possible. Furthermore, from a statistical point of view, the parametric structure of the mixtures of the Erlang distribution offers some advantages compared with the whole over‐parametrized family of phase‐type distributions. Given the observed claim arrivals and claim sizes, we show how to estimate the ruin probabilities, as a function of the initial capital, and predictive intervals that give a measure of the uncertainty in the estimations.     

浅析当代男子优秀三级跳远运动员三跳比例

本文以具有当今世界水平男子优秀三级跳远选手的比赛成绩为依据,运用不同时期三级跳远最佳三跳组合的模式,研究了三级跳远成绩与三跳比例的关系,找出了影响不同类型运动员三级跳远比例及成绩的主要优势因素,论述了三级跳远运动员应有不同的中心训练任务和训练方法。     

Bayesian regression under combinations of constraints

A Bayesian method for regression under several types of constraints is proposed. The constraints can be range-restricted and include shape restrictions, constraints on the value of the regression function, smoothness conditions and combinations of these types of constraints. The support of the prior distribution is included in the set of piecewise linear functions. It is shown that the proposed prior can be arbitrarily close to the distribution induced by the addition of a polynomial plus an (m−1)-fold integrated Brownian motion. Hence, despite its piecewise linearity, the regression function behaves (approximately) like an m−1 times continuously differentiable random function. Furthermore, thanks to the piecewise linear property, many combinations of constraints can easily be considered. The regression function is estimated by the posterior mode computed by a simulated annealing algorithm. The constraints on the shape and the values of the regression function are taken into account thanks to the proposal distribution, while the smoothness condition is handled by the acceptation step. Simulations from the posterior distribution are obtained by a Gibbs sampling algorithm.     

Markov-chain monte carlo: Some practical implications of theoretical results

We review and discuss some recent progress in the theory of Markov-chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.     

Statistical Issues in Fisheries' Stock Assessments*

Decisions concerning the management of fisheries are founded on confidence statements for interest parameters such as biomass and exploitation rate, derived from complex structural models that describe the dynamics of fisheries. We identify four generic statistical issues and focus on how they impact on the reliability of those confidence statements: (a) parameters for which the data have little or no information; (b) competing structural relationships; (c) weighting of observations; and (d) alternative methods for computing confidence statements. Our purpose is to give an exposition of how these issues impact on fisheries' analyses, with the intent of stimulating thought on more effective alternatives. We describe the fisheries' management context and use two specific studies to illustrate how these generic statistical issues impact on fisheries assessment results. It is demonstrated that these statistical issues can have a profound impact on fishery management decisions and that established approaches to handle them have not been fully developed.