季节时间序列理论发展综述

随着社会的进步,统计数据由过去的年度数据变为如今的季度、月度和日度数据,有些以实时交易为基础的超高频金融数据达到了按秒为间隔的频率,这些数据被称为季节时间序列。季节时间序列研究已经成为近十年来经济计量学和统计学中的热点,Journal of Econometrics(1993,volume55)就此问题进行了专题讨论。本文按照历史发展顺序对季节性时间序列理论进行了系统地介绍,并对这一领域的前沿热点问题进行了评述和展望。

常见的心理平衡方式

趋向平衡,是大自然的普遍规律。而平衡又在不断地被打破,不平衡与平衡相伴相随,交替出现,于是出现了不平衡——平衡——新的不平衡——新的平衡这样螺旋式的周期性过程。心理平衡也不例外,在现实生活中,人的大脑会对不断出现的各种外来刺激作出反应,形成不同的精神需要,使得心理出现不平衡,并产生相应的补偿行为,从而使心理趋向平衡。但是不同的社会人群,由于一定文化模式的制约。

Iterative Learning Model Predictive Control for a Class of Continuous/Batch Processes

An iterative learning model predictive control （ILMPC） technique is applied to a class of continuous/batch processes. Such processes are characterized by the operations of batch processes generating periodic strong disturbances to the continuous processes and traditional regulatory controllers are unable to eliminate these periodic disturbances. ILMPC integrates the feature of iterative learning control （ILC） handling repetitive signal and the flexibility of model predictive control （MPC）. By on-line monitoring the operation status of batch processes, an event-driven iterative learning algorithm for batch repetitive disturbances is initiated and the soft constraints are adjusted timely as the feasible region is away from the desired operating zone. The results of an industrial application show that the proposed ILMPC method is effective for a class of continuous/batch processes.

Effects of Mechanical Impacts on Hatchability of Broiler Breeders

Transporting hatching eggs from Hungary and incubating them abroad revealed lower hatchability compared to when the eggs were incubated in Hungary. Following transport, there were higher embryo losses and, notably, more malformed embryos. The aim of these initial trials was to determine if a testing device （crazy fit massage machine （CFM machine）） was able to replicate and model the mechanical impacts experienced during transport and reproduce the reduction in hatchability and increase the level of malformed embryos as observed in commercial practice. Tinytag~ high sensitivity shock and vibration loggers were used to monitor the impacts under field and trial conditions. Applying single 10 min treatments on the CFM machine, which used the same frequency （10-30 Hz） as the eggs experience under field conditions, induced the negative effect of transport, and lower hatching results were experienced. Three trials were conducted. Treated eggs in Trials 1 and 2 received automatically and periodical changing vibration in a range between 10-30 Hz for 10 min while in Trial 3 two different levels of impact were applied at 20 Hz and 30 Hz, respectively. Hatchability decreased due to the treatment significatly only in Trial 3. Significant differences were also detected in early dead levels in Trials 2 and 3 and the occurrences of malformation in Trials 1 and 3. All these results are in accordance with the field experience. Thus, the trials which examined the equipment were able to produce mechanical impacts that were repeatable in order to set up statistically reliable trials on hatching eggs.

Minimax Estimation Problem for Periodically Correlated Stochastic Processes

The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.

Stationary and Non-stationary Self-Induced Vibrations in Waveguiding Systems

With the use of a wave model, the non-linear problem about realization of the Poincare-Hopf bifurcations in waveguiding systems is stated. The constitutive non-linear differential equations are deduced, the methods for their solution are elaborated. The example of torsion wave propagation in an elongated drill string is considered. Computer simulation of auto-oscillation generation in the examined system is performed for the cases of stationary and non-stationary variations of the perturbation parameter. The diapason of the drilling rotation velocity values corresponding to regimes of stable self-excited periodic motions of the system is found. This domain is shown to be limited by the states of the Poincare-Hopf bifurcations. Owing to the feature that the stated problem is singularly perturbed, the autovibrations are of relaxation type with fast and slow motions. Influence of the length of the uniform and articulated drill strings on the bifurcation values of their angular velocities of generation and accomplishment of the auto-oscillation processes in the drill strings is discussed.

Optimal Investment with Multiple Risky Assets for an Insurer with Modified Periodic Risk Process

This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic risk process is perturbed by a standard Brownian motion.The insurer can invest in multiple risky assets and one risk-free asset and the correlations between the risky assets and the risk process are considered.Optimal strategy is obtained explicitly,which is a function of time and related to the risk process.The effects of market parameters on the optimal strategy are discussed and a numerical example is also given.

Some limit theorems of killed Brownian motion

In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.