Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

离散时间不完全金融市场中未定权益的定价

对一类连续时间不完全市场（其中的股票价格由Brown运动驱动），ElKarouiandQuenez[1]讨论了一般的不可达未定权益的定价问题．本文利用FollmerandKabanov[2]建立的分解定理，证明[1]中关于买方与卖方价格过程的结果与方法适用于一般的离散时间不完全金融市场（定理1）．特别，关于买方与卖方价格我们给出另一种合理的解释（定理3）．     

凑合反推法──流体力学变分原理建立的一条新途径

凑合反推法是刘商联系统方法[1]的进一步发展，应用这种方法可以方便地构造各种亚广义变分原理及广义变分原理，并可以消除临界变分现象．对于任何二维守恒型流体力学方程，作者推导得到了其广义变分通用公式．几个实例证明这种方法是有效的、简单的，并具有普遍的意义．     

宏观调控“两难”新环境下中国CPI运行定量分析——基于改进的BP神经网络

当前,我国经济继续回升向好,但宏观调控面临的"两难"问题增多.如何防止经济快速下滑和防范通货膨胀成为当前宏观经济决策的重要内容,准确预见我国价格运行趋势对宏观决策具有十分重要的意义.1997年和2008年分别发生了对世界经济发展影响深远的两次金融危机.两次金融危机发生后,中国政府均实施了大规模的经济刺激计划,但反映经济运行的主要宏观经济指标CPI月度指数从危机发生当年的次年开始,步入了长达数月负区间运行.研究发现1997年金融危机发生前后月度CPI指数运行相关度非常高,2008年金融危机发生当年月度CPI指数与2007年、2009年月度CPI指数运行相关度也非常高.对此,运用改进的BP神经网络模型对1995-1999年中国月度CPI指数进行学习,以2006-2009年月度CPI指数数据为基础,对2010年中国下半年月度CPI指数进行了预测,显示全年CPI指数预计为102.85.对此,认为2010年我国面临适度的通胀压力,提出了应对政策建议.     

Boom and bust in continuous time evolving economic model

We show that a simple model of a spatially resolved evolving economic system, which has a steady state under simultaneous updating, shows stable oscillations in price when updated asynchronously. The oscillations arise from a gradual decline of the mean price due to competition among sellers competing for the same resource. This lowers profitability and hence population but is followed by a sharp rise as speculative sellers invade the large un-inhabited areas. This cycle then begins again.     

Clusters in weighted macroeconomic networks: the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990–2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.     

”Illusion of control” in Time-Horizon Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the “illusion of control” in certain set-ups a priori defined to emphasize the importance of optimization. An erratum to this article is available at .     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

The Stock Market Model with Delayed Information Impact from a Socioeconomic View

Finding the critical factor and possible “Newton’s laws” in financial markets has been an important issue. However, with the development of information and communication technologies, financial models are becoming more realistic but complex, contradicting the objective law “Greatest truths are the simplest.” Therefore, this paper presents an evolutionary model independent of micro features and attempts to discover the most critical factor. In the model, information is the only critical factor, and stock price is the emergence of collective behavior. The statistical properties of the model are significantly similar to the real market. It also explains the correlations of stocks within an industry, which provides a new idea for studying critical factors and core structures in the financial markets.     

财务重述对分析师预测行为的影响研究

本文以我国2005-2009年间A股市场发生年度财务报表重述的公司并结合相应的分析师预测数据作为样本,分别考察了财务重述和财务重述调整金额对分析师跟进及预测特征的影响。多元回归结果表明:财务重述会减少分析师跟进、增加分析师预测误差,重述调减以前年度损益的程度越大,分析师预测的分歧和误差就越大;而财务重述增加分析师预测分歧、重述调整金额影响分析师跟进的假设却未得到证实。本研究发展了财务重述、分析师预测的研究内容,为提高公司财务报告质量、规范分析师行业提供了相应的思路。