ON THE UNIMODALITY OF THE EXACT LIKELIHOOD FUNCTION FOR NORMAL AR(2) SERIES

Abstract. For stationary second-order autoregressive normal processes, the conjecture of uniqueness of the solution of the exact likelihood equations is examined. A sufficient condition for uniqueness is given; this condition is satisfied with very high probability if the number of observations is not extremely small. Moreover, it is shown that not more than two maxima may exist. Examples of data which actually produce a likelihood function with two local maxima are given.     

SOME PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE SIMULTANEOUS SWITCHING AUTOREGRESSIVE MODEL

Abstract. The simultaneous switching autoregressive (SSAR) model proposed by Kunitomo and Sato (A non-linearity in economic time series and disequilibrium econometric models. In Theory and Application of Mathematical Statistics (ed. A. Takemura). Tokyo:University of Tokyo Press (in Japanese), 1994; Asymmetry in economic time series and simultaneous switching autoregressive model. Struct. Change Econ. Dyn. , forthcoming (1994).) is a Markovian non-linear time series model. We investigate the finite sample as well as the asymptotic properties of the least squares estimator and the maximum likelihood (ML) estimator. Due to a specific simultaneity involved in the SSAR model, the least squares estimator is badly biased. However, the ML estimator under the assumption of Gaussian disturbances gives reasonable estimates.     

Maximum principle for mean-field jump–diffusion stochastic delay differential equations and its application to finance

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump–diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean–variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean–variance problem without delays.     

An understanding of high entropy alloys from phase diagram calculations

The concept of High Entropy Alloy (HEA) is understood from the point of view of phase diagram calculation. The role of entropy of mixing on the phase stability is discussed for both ideal and non-ideal solid solution phases. The relative stability of a solid solution phase and line compounds is illustrated using hypothetical systems. Calculated binary and multicomponent phase diagrams are used to explain the phenomena observed experimentally for HEAs. The potential of using the CALPHAD (CALculation of PHAse Diagrams) approach in aiding the design of alloys with multiple key components is also discussed.     

淮河流域水资源短缺风险评估与时空分析

根据2003-2013年淮河流域五省的降水量、径流系数、人均水资源量、人均GDP、人口密度等相关数据,构建水资源短缺风险评价体系,用熵权法对指标赋值,运用可变模糊模型对淮河流域及各省的水资源短缺风险进行评估和时空差异分析。结果表明:2003-2013年间淮河流域水资源短缺风险值总体较高,且呈缓慢的增长趋势,2004年降水较少,风险值达到最高;十年间河南省风险增加最为明显,而山东省较为稳定,风险增加也最低;在淮河流域五个区域中,河南省的风险程度最高,达到3.52;江苏省、山东省次之;安徽省和湖北省相对较低,达到2.86和2.51。水资源短缺风险二级指标分析发现,危险性最强的是河南省,安徽省最小;水资源短缺易损性最强的是山东省,湖北省最小;水资源短缺暴露性最强的是江苏省,山东省最小;水资源短缺可恢复性最好的是湖北省,河南省最差。同时,所有评价指标中人口密度、人均GDP、降水量对水资源短缺风险的影响较大。     

Personalized identification of abdominal wall hernia meshes on computed tomography

An abdominal wall hernia is a protrusion of the intestine through an opening or area of weakness in the abdominal wall. Correct pre-operative identification of abdominal wall hernia meshes could help surgeons adjust the surgical plan to meet the expected difficulty and morbidity of operating through or removing the previous mesh. First, we present herein for the first time the application of image analysis for automated identification of hernia meshes. Second, we discuss the novel development of a new entropy-based image texture feature using geostatistics and indicator kriging. Third, we seek to enhance the hernia mesh identification by combining the new texture feature with the gray-level co-occurrence matrix feature of the image. The two features can characterize complementary information of anatomic details of the abdominal hernia wall and its mesh on computed tomography. Experimental results have demonstrated the effectiveness of the proposed study. The new computational tool has potential for personalized mesh identification which can assist surgeons in the diagnosis and repair of complex abdominal wall hernias.     

A RANDOM PARAMETER PROCESS FOR MODELING AND FORECASTING TIME SERIES

Abstract. A generalized autoregressive (GAR) process {Z ( t ) ; t = 0 , ±1, …} is defined to satisfy the recurrence relation Z(t) = A_θ (t)Z (t -l)+ u( t ), where {A_θ(t); t = 0,±1, …} is itself a stochastic process depending on a vector parameter θ and where {u( t ); t = 0, ±1, …} is white noise with Eu ² ( t ) = a ². This paper develops theory and methodology and implementing the class of GAR processes for time series modeling and forecasting. Conditions on the 'parameter process' { A _θ ( t ); t = 0, ±1, …} are obtained for the existence of a GAR process; necessary and sufficient conditions on { A_θ ( t ) ; t = 0, ±1, …} for existence of a stationary GAR process are also obtained. Procedures are developed for computing maximum likelihood estimates of the parameters 0 and u² and for computing the minimum mean squared error forecasts for GAR processes.     

一种不确定图中最可靠最大流问题的解决方案

最可靠最大流是不确定图中可靠性最高的最大流,它是传统最大流问题在不确定图上的自然延伸.现有的最可靠最大流算法SDBA时间复杂性较高,无法满足实际中不同应用的需求,为此,文中提出一种具有普遍适用性的最可靠最大流解决方案.该方案包含面向不同需求的3种算法:基于负权群落消去的NWCE算法、基于时间约束优先单环消去的SPEA-t算法和基于概率阈值约束优先单环消去的SPEA-p算法.其中,NWCE算法借鉴最小费用最大流的"流平移"思想并基于文中提出的负权群落概念,在辅助剩余图中不断地消去可使可靠性增加而流量不变的负权群落,可证当消去所有负权群落时对应的最大流即为最可靠最大流.根据负权群落中由单环组成的群落占很高比例且相对于多环组成的群落更易查找和消去的性质,同时考虑到NWCE算法为了获得最优解,往往为了消去最后少数几个对概率提高贡献很小的负权群落却花费了很长时间的现象,提出SPEA-t和SPEA-p两种快速近似算法,前者是以规定时间内尽可能逼近最优解为目标,后者是以最少时间达到预设的概率阈值为目标,它们都采用了优先消去概率-时间效益较好的单环群落的策略,加快对最优解的逼近速度,减少或放弃时间开销较大的多环群落的消去,以满足那些对算法时间性能要求很高而结果以近似最优即可的应用需求.实验表明,相对于SDBA算法,NWCE算法结合概率剪枝策略在时间性能上有了数量级的提高,而SPEA-t算法和SPEA-p算法则具有更高的性能和更好的适用性.     

Selecting the forgetting factor in subset autoregressive modelling

Abstract. Conventional methods to determine the forgetting factors in autoregressive (AR) models are mostly based on arbitrary or personal choices. In this paper, we present two procedures which can be used to select the forgetting factor in subset AR modelling. The first procedure uses the bootstrap to determine the value of a fixed forgetting factor. The second procedure starts from this base and applies the time-recursive maximum likelihood estimation to a variable forgetting factor. In one illustration using real exchange rates, we demonstrate the effect of the forgetting factor in subset AR modelling on ex ante forecasting of non-stationary time series. In a second illustration, these two procedures are applied to time-update forecasts for a stock market index. Subset AR models not including a forgetting factor act as a set of benchmarks for assessing ex ante forecasting performance, and consistently improved forecasting performance is demonstrated for these proposed procedures.