摘要
2005年7月,我国进行了一次重要的汇率制度改革,确立了人民币汇率形成机制市场化的长期发展目标。此后,政府又陆续颁布了许多配套实施细则。在此背景下,人民币汇率出现了单边升值趋势,而且汇率波动的频度和幅度明显扩大。直到2008年10月,单边升值趋势在全球金融危机的影响下才开始逆转。这不仅给人民币外汇市场的稳定性带来了严峻的考验,同时也对政府职能转变、汇率制度建设、央行市场化干预手段提出了更高的要求。
本论文的研究主题是：“汇改”前后,人民币汇率的运动是否具有本质上的差异?果真如此,汇率运动的新特征和新规律究竟是什么?在此基础上,央行进行外汇市场干预时,可以选择怎样的干预目标,在有效地抑制市场的过度波动的同时,减小汇率水平的扭曲度?
在理论研究部分,首先对传统的汇率理论的发展历史进行回顾和梳理,并分析指出传统的汇率决定理论面临的主要问题是对现实中汇率异常波动的解释力和预测能力低下。导致这种现象的主要原因是：传统的汇率决定理论的前提假设“有效市场假说”和“理性预期假说”过于理想化,与经济运行的现实情况差异较大。另外,传统的汇率决定理论采用的线性范式与汇率运动的非线性特征不相吻合。然后,对混沌理论的研究现状、基本概念、重要模型等进行了介绍。这是本文研究的理论基础和方法论。
由于境外NDF汇率对境内即期汇率具有重要的影响作用,在实证研究部分,本文首先对“汇改”之后境内即期汇率和境外NDF汇率现状进行了定性描述和统计分析。结果显示它们具有明显的“尖峰厚尾”和“波动聚集效应”特征。这也否定了“有效市场假说”的结论。然后,选择人民币兑美元汇率时间序列作为研究对象,以Simon Haykin混沌判据为标准,进行实证检验。检验的结果表明：“汇改”之后,人民币汇率波动具有明显的混沌动力学属性。
在实证检验的基础上,本文尝试着对汇率混沌的内在机理给予理论上的解释和模型证明：汇率的混沌是外汇市场上的信息流在异质性交易者的作用下,通过内在的非线性关系,形成汇率价格信号,引起汇率波动的结果,这是混沌系统特有的内随机性。然后,运用该结论,结合“汇改”的实际情况,对人民币汇率的混沌现象进行了相应的分析。
通过上述分析,本文结合混沌控制的原理和方法,建立了引入央行干预因素的汇率混沌模型,并对央行干预目标和有效性展开深入的讨论。研究表明：在汇率混沌的条件下,“逆风而动”干预不仅无法抑制汇率的波动,也不能减少汇率水平的扭曲度。如果央行选择“目标长期基本因素值”干预,并且保证充分的干预力度,那么,央行可以在抑制汇率波动的同时减少汇率扭曲。另外,央行选择“定常反馈”干预,可以在保持一定汇率扭曲程度的基础上,成功抑制汇率的波动,实现特定的经济目标。最后,根据汇率混沌的实证检验、理论解释和对央行干预模型分析的有关结果,本文给出相应的政策建议。
The China exchange rate system was reformed substantially in July 2005, with the set up of long-term development target of market-oriented RMB exchange rate formation mechanism. Thereafter, a series matching implementation rules have been promulgated by the governmental and RMB has kept appreciating, with increasing fluctuation frequency and extent, until October 2008. RMB stopped appreciating due to the influence of global financial crisis, which not only examines the stability of RMB foreign exchange market but also puts strict requirements for transformation of government function, development of exchange rate system, intervention manners of the central bank, etc.
The paper discusses whether changes in RMB exchange rate show difference prior to and after the reform of RMB exchange rate. If it does, what are new features and rules of changes in RMB exchange rate? What targets are when the central bank intervenes in the foreign exchange market so as to effectively reduce over-fluctuation and minimize the exchange rate misalignment?
In the part of theory research, the paper reviews the traditional theory of exchange rate, which is weak in interpreting and forecasting the abnormal fluctuation in real world for the following reasons:firstly, the assumptions of traditional theory, effective market hypothesis and rational expectation hypothesis, are too idea to be different with the actual economy; secondly, the linear paradigm applied by the traditional theory conflict with the non-linear character of changes of exchange rate. Besides, the research actuality, basic concept and key model of chaos theory are introduced, which are the research rational and methodology of this paper.
In the part of empirical study, the paper qualitatively analyzes the actuality of RMB spot rate and oversea NDF rate. The result shows that both of them are characterized of obvious "cute peak and fat tail" and "volatility clustering effect" which deny the conclusion of effective market hypothesis. Then, empirical test is executed by selecting the time series of RMB:USD exchange rate and applying Simon Haykin's chaos criterion as standards. The test result implies that changes in exchange rate are characterized of chaos dynamics after reform.
On the basis of empirical study, the paper attempts to theoretically explain the intrinsic mechanism of chaos exchange rate and prove with models. Chaos exchange rate results from movements of exchange rate along with the signal of exchange rate price through intrinsic non-linear relationship when the information flow of foreign exchange rate is exposed to the effect of the trader heterogeneity. By applying this conclusion and combining the actual condition of exchange rate reform, the paper analyzes the chaos of RMB exchange rate.
Through the aforesaid analysis and in combination of rational and method of chaos control, the paper establishes an exchange rate chaos model where the intervene factors of central bank is introduced. "Leaning Against the Wind" intervention fails to restrain fluctuation of exchange rate and minimize exchange rate misalignment. If the central bank selects to "Targeting Long-run Fundamentals" intervention and ensures sufficiently intervening level, both of two targets would be realized. Finally, the paper proposes some policies in accordance with the analysis result of empirical text of chaos exchange rate, theatrical explanation and intervening model of central bank.
引文
3. Fama E F. The Behavior of Stock Markets Prices [J]. Journal of Business,1965,38:34-105
4. Meese R A, Rogoff R. Empirical Exchange RateModelsof the Seventies:Do They Fit Out of Sample[J]. Journal of International Economics,1983,14:3-24.
5.Mussa M. Empirical Regularities in the Behavior of Exchange Rate and Theories of the Foreign Exchange Market [A]. in:Policies for Employment,Prices, and Exchange Rates[C]. Karl Brunner, Allan H Meltzer. (eds), Carnegie-Rochester Conference Series on Public Policy,1979
6. Frenkel J A. Flexible Exchange Rate, Prices, and the Role ofNews:Lessons from the 1970 s[J]. Journal of Political Economy,1981,89 (4):665-705.
7. Edwards S. Floating Exchange Rates, Expectations and New Information [J]. Journal of Monetary Economics,1983,11:321-36
8. Blanchard 0 J. Speculative Bubbles, Crashes and Rational Expectations [J]. Economic Letters,1979,3:387-89
9. ObstfeldM, Rogoff K. The Six Major Puzzles in International Macroeconomics:Is There A Common Cause [A]. in:NBER Macroeconomics Annual [C]. Bernanke B, Rogoff K. (eds), CambridgeMA,2000
10. Lyons R. The Microstructure Approach to Exchange Rate [J]. MIT Press.2001
11. EvansM, Lyons R. Order Flow and Exchange-Rate Dynamics [J]. Journal of Political Economy,2002,110: 170-80
12. Frankel J A, Froot K A. Chartists. Fundamentalists.and Trading in the Foreign Exchange Market [J]. American Economic Review,1990.80:181-5.
14. Day R. and Shafer J. "Keynesian Chaos" [J]. Journal of Macroeconomics,1985(7):277-295
15. Barnett W. and Chen P., "Deterministic Chaos and Fractal Attractors as Tools for Nonparametric Dynamical Econometric Inference:With an Application to the Division Monetary Aggregates"[J]. Mathematical and Computer Modeling,1988(10)275-296
16. Chen P., "Empirical and Theoretical Economic Chaos"[J]. System Dynamics Review,1988(4)81-108
17. Moshiri S.."Testing for Deterministic Chaos in Futures Crude Oil Price:Does Neural Network Lead to Better Forecast?" Economics. Working Paper.2004.5
18. Hsieh D. "The Statistical Property of Daily Foreign Exchange Rates:1974-1983"[J]. Journal of International Economics,1988,(24):132-145
19. Hsieh D. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates"[J]. Journal Business,1989. (62):339-359
20. Meese R.A. and Rose R.K., "An Empirical Assessment of Nonlinear ties in Models of Exchange Rate Determination"[J]. Review of Economic Studies,1991,(58)603-619
21 Frankel J. and Froot K., "Understanding the U.S. Dollar in the Eighties:The Expectation of Chartists and Fundamentals"[J]. Economic Record,Supplement,1986(10):24-38
22 Frankel J. and Froot K., "Forward Discount Bias:ls it an Exchange Risk Premium"[J].Quarterly Journal of Economics,1989(104)139-161
23. De Grauwe P, Dewachter H, EmbrechtsM. Exchange Rate Theory:ChaoticModels of Foreign Exchange Markets [M]. Blackwell Publishers.1993
24.埃德加.E.彼德斯.分形市场分析-将混沌理论应用到投资和经济理论上[M].北京：经济科学出版社,2002.
25. Mandelbrot B., "Fractals and Scaling in Finance"[M]. New York, USA.Springer,1997:P51-62
26. Cecen A. and Erkal C., "Distinguishing Between Stochastic and Deteministic Behavior in High Frequency Foreign Exchange rate returns:Can Nonlinear Dynamics Help Forecasting"[J]. International Journal of Forecasting,1996(12)465-473
27. Marties A.K., "The Application of Chaos Theory in the Philippine Foreign Exchange Market"[J]. Khanser Publishing House,1999(12)65-68
28. Richards G. "The Fractal Structure of Exchange Rates:Measurement and Forecasting"[J].Journal of International Financial Markets,2000(10):163-180
29. Michael Bask., "Dimensions, and Lyapunov Exponents From Exchange Rates Series"[J]. Chaos,Solutions and Fractals,1996(12):2199-2214
30. Michael Bask., "Deteriminsitic Chaos in Exchange Rates?"[J]. Umea Economices Studies,1998(13):465-470
31. Michael Bask., "A Positive Lyapunov Exponent in Swedish Exchange Rates?"[J]. Chaos.Solutions and Fractals,2002(14)1295-1304
32. Schwatz and Yousefi., "On Complex Behavior and Exchange Rates Dynamics"[.l].Chaos,Solution and Fractals,2003(18)503-523
33. Dean Taylor. "Official Intervention in the Foreign Exchange Market, or, Bet against the Central Bank"[J] Journal of Political Economy,1982,90(2),356-368
34. Schwartz, A.,2000. "The rise and the fall of foreign exchange market intervention as a policy tool" [J]. Journal of Financial Services Research 18,319-339.
35. Kathryn M.dominguez, "Does Central Bank Intervention Increase the Volatility of Foreign Exchange Rates?" (1993)NBER:WorkingPaper No.4532
36. Weston R. and Permachandran P., "A Chaos Analysis of the New Zealand Exchange Rates 1985-2004"[J]. Emerging Financial Markets and Services Conference,2004(5)261-268
37. Wieland C., "Controlling Chaos in Higher Dimensional Maps with Constant Feedback:An Analytical Approach". Physical Review,2002(66)58-75
38. Wieland C. and Westerhott F.H., "Exchange Rates Dynamics,Central Bank Interventions and Chaos Control Methods"[J]. Modeling, Computing and mastering Complexity,2003(22):22-26
39.杨培才等人(1992)：“经济混沌的实例及可预报性”
40.王军等(1993)：“标准普尔500指数(S&P 500)的混沌吸引子”
41.刘洪：《系统工程理论方法应用》
42.黄登仕、李后强：《非线性经济学的理论与方法》
43.方锦清,“非线性控制与混沌控制论---略谈与现代控制论的结合”[J].自然杂志,1994(3)：147-152
44.张永安,“汇率波动的奇异吸引子测定及其应用分析”[J].西安交通大学学报,1998(8):92～95
45.戴国强,徐龙炳,陆蓉,“国际汇率波动的非线性探索及其政策意义”[J].国际金融研究,1999(10)：9-15
46徐瑞娥：关于混沌学和混沌经济学的探索[J]《财政研究》2000年第4期
47.陆前进：汇率理论研究的新方法---混沌理论及其评述[J]《国际金融研究》2000年第2期
48.崔孟修：汇率决定的混沌分析方法[J]《管理世界》双月刊2001年第1期
49.周作领,舒元,“混沌经济学---混沌与分形”[J].数学的实践与认识,2003(3)：30-33
50.马军海,盛昭瀚,陈春旺,“经济时序动力系统的分形及混沌特性研究”[J].系统工程学报,2000(15)：13-18
51.王海燕,盛昭瀚,“多变量时间学列复杂系统的相空间重构”[J].东南大学学报,2003(35)15-18
52.徐科军,“资本市场的混沌与分形---从有效市场假说到分形市场假说”[J].河南金融管理干部学院学报,2002(3)29-3]
53.谢赤,杨妮,孙柏：“汇率时间序列混沌动力学特征及实证”[J].系统工程理论与实践,2008年8月
54.谢赤,罗福来,孙柏：“基于混沌分析的人民币兑美元汇率行为研究”[J].湘潭大学学报2008年7月
55.殷光伟.“小波与混理论相结合的汇率预测”[J].《商场现代化》2009年2月(中旬刊)总第566
59 Thomas Gehrig and Lukas Menkhoff, "The Use of Flow Analysis in Foreign Exchange:Exploratorv Evidence",2001
63 R.Day and W.Huang. Bulls.Bear and market sheep. Journal of Economic Behavior and Organization 14(1990). 299-329
64 W.Huang and R.day. "Chaotically switching bear and bull markets:The derivation of stock price distributions from behavioral rules". Nonliner Dynamic and Evolutionary Economics. Oxford University Press. Oxford.1993. pp.169-182
65 M A. Torkamani, S. Mahmoodzadeh, S. Pourroostaei, and C. Lucas, "Chaos Theory and Application in Foreign Exchange Rates vs. IRR (Iranian Rial)". [J]. International Journal of Human and Social Sciences,2007,1;3
66雷强.李争争.人民币汇率的混沌特征.[J].科技管理研究.2009年第7期
67 Allen.H. and M.P. Taylor,Chart,Noise and Fundamentals in the London Foreign Exchange Market,[J] Economic Journal,1990.400:49-59
68 Dean Taylor, "Official Intervention in the Foreign Exchange Market, or, Bet against the Central Bank"[J] Journal of Political Economy,1982.90(2),356-368
69 Schwartz, A.,2000. "The rise and the fall of foreign exchange market intervention as a policy tool "[J]. Journal of Financial Services Research 18,319-339.
70 Dominguez, Kathryn M. (1993) "Does Central Bank Intervention Increase the Volatility of Foreign Exchange Rates?" NBER Working Paper No.4532.
71 Kathryn M. Dominguez, "Central Bank Intervention and Exchange Rate Volatility".[J] Journal of International Money and Finance 17(1998)161-190
72刁峰,中国央行外汇干预市场干预目标的实证研究,南开经济研究,2001年第6期,P56-59
73杨金梅,论我国央行外汇干预与冲销操作,复旦大学博士论文,2007年7月20日
74 T. Gehrig and L. Menkhoff, "The Use of Flow Analysis in Foreign Exchange:Exploratory Evidence",2001,
75 Frank H. Westerhoff. "The Impact of Flow Analysis on Exchange Rate Dynamics",2005
76 Wieland,C.. 2002. "Controlling chaos in higher dimensional maps with constant feedback:an analytical approach " [J].Physical Review E 66.016205.1-8.
77见边绪宝,新外汇管理条例有助于防范和打击热钱[N],证券时报,2008-8-8
78麦金农(2003)《罗纳德。麦金农谈中国的汇率》,“人民币汇率问题国际研讨会,,大会材料,原载《亚洲华尔街日报》2003年6月27日。
[1]埃德加.E.彼德斯.“分形市场分析-将混沌理论应用到投资和经济理论”[M].北京：经济科学出版社,2002.
[2]崔孟修：“汇率决定的混沌分析方法”[J]《管理世界》双月刊2001年第1期
[3]戴国强,徐龙炳,陆蓉,“国际汇率波动的非线性探索及其政策意义”[J].国际金融研究,1999(10)：9-15
[4]刁峰,“中国央行外汇干预市场干预目标的实证研究”,南开经济研究,2001年第6期,P56-59
[5]方锦清,“非线性控制与混沌控制论---略谈与现代控制论的结合”[J].自然杂志,1994(3)：147～152
[6]黄登仕、李后强：《非线性经济学的理论与方法》
[7]雷强,李争争,“人民币汇率的混沌特征”[J].科技管理研究,2009年第7期
[8]刘洪：《系统工程理论方法应用》
[9]陆前进：“汇率理论研究的新方法---混沌理论及其评述”[J]《国际金融研究》2000年第2期
[10]马军海,盛昭瀚,陈春旺,“经济时序动力系统的分形及混沌特性研究”[J].系统工程学报,2000(15)：13-18
[11]王海燕,盛昭瀚,“多变量时间学列复杂系统的相空间重构”[J].东南大学学报,2003(35)15-18
[12]王军等(1993)：“标准普尔500指数(s&P 500)的混沌吸引子’
[13]谢赤,罗福来,孙柏：“基于混沌分析的人民币兑美元汇率行为研究”[J].湘潭大学学报2008年7月
[14]谢赤,杨妮,孙柏：“汇率时间序列混沌动力学特征及实证”[J].系统工程理论与实践,2008年8月
[15]徐科军,“资本市场的混沌与分形---从有效市场假说到分形市场假说”[J].河南金融管理干部学院学报,2002(3)29～31
[16]徐瑞娥：“关于混沌学和混沌经济学的探索”[J]《财政研究》2000年第4期
[17]杨培才等人(1992)：“经济混沌的实例及可预报性”
[18]杨金梅,“论我国央行外汇干预与冲销操作”,复旦大学博士论文,2007年7月20日
[19]殷光伟,“小波与混理论相结合的汇率预测”[J].《商场现代化》2009年2月(中旬刊)总第566
[20]张永安,“汇率波动的奇异吸引子测定及其应用分析”[J].西安交通大学学报,1998(8)：92～95
[21]周作领,舒元,“混沌经济学---混沌与分形”[J].数学的实践与认识,2003(3)：30-33
[22]Allen,H. and M.P. Taylor, "Chart,Noise and Fundamentals in the London Foreign Exchange Market"[J] Economic Journal,1990,400:49-59
[23]Barnett W. and Chen P., "Deterministic Chaos and Fractal Attractors as Tools for Nonparametric Dynamical Econometric Inference:With an Application to the Division Monetary Aggregates "[J]. Mathematical and Computer Modeling,1988(10)275-296
[24]Blanchard O J. "Speculative Bubbles, Crashes and Rational Expectations " [J]. Economic Letters,1979,3:387-89
[25]Cecen A. and Erkal C., "Distinguishing Between Stochastic and Deteministic Behavior in High Frequency Foreign Exchange rate returns:Can Nonlinear Dynamics Help Forecasting "[J]. International Journal of Forecasting,1996(12)465-473
[26]Chen P., "Empirical and Theoretical Economic Chaos "[J]. System Dynamics Review,1988 (4)81-108
[27]Day R. and Shafer J. "Keynesian Chaos " [J]. Journal of Macroeconomics,1985(7):277-295
[28]Dean Taylor, "Official Intervention in the Foreign Exchange Market, or, Bet against the Central Bank "[J] Journal of Political Economy,1982,90(2),356-368
[29]De Grauwe P, Dewachter H, EmbrechtsM. "Exchange Rate Theory:Chaotic Models of Foreign Exchange Markets " [M]. Blackwell Publishers,1993
[30]Dominguez, Kathryn M. (1993) "Does Central Bank Intervention Increase the Volatility of Foreign Exchange Rates? " NBER Working Paper No.4532.
[31]Edwards S. "Floating Exchange Rates, Expectations and New Information " [J]. Journal of Monetary Economics,1983,11:321-36
[32]Evans M, Lyons R. "Order Flow and Exchange-Rate Dynamics" [J]. Journal of Political Economy,2002,110:170-80
[33]Fama E F. "The Behavior of Stock Markets Prices" [J]. Journal of Business,1965,38:34-105
[34]Frank H. Westerhoff, "The Impact of Flow Analysis on Exchange Rate Dynamics ",2005
[35]Frankel J. and Froot K., "Understanding the U.S. Dollar in the Eighties:The Expectation of Chartists and Fundamentals"[J]. Economic Record,Supplement,1986(10):24-38
[36]Frankel J. and Froot K., "Forward Discount Bias:Is it an Exchange Risk Premium "[J]. Quarterly Journal of Economics,1989(104)139-161
[37]Frenkel J A. "Flexible Exchange Rate, Prices, and the Role of News:Lessons from the 1970 s"[J]. Journal of Political Economy,1981,89 (4):665-705.
[38]Frankel J A, Froot K A. "Chartists, Fundamentalists,and Trading in the Foreign Exchange Market" [J]. American Economic Review,1990,80:181-5.
[39]Hsieh D. "The-Statistical Property of Daily Foreign Exchange Rates:1974-1983 "[J]. Journal of International Economics,1988,(24):132-145
[40]Hsieh D. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates "[J]. Journal Business,1989, (62):339-359
[41]Kathryn M.dominguez, "Does Central Bank Intervention Increase the Volatility of Foreign Exchange Rates? " (1993)NBER:WorkingPaper No.4532
[42]Kathryn M. Dominguez, "Central Bank Intervention and Exchange Rate Volatility",[J] Journal of International Money and Finance 17(1998)161-190
[43]Lyons R. "The Microstructure Approach to Exchange Rate " [J]. MIT Press,2001
[44]M. A. Torkamani, S. Mahmoodzadeh, S. Pourroostaei, and C. Lucas, "Chaos Theory and Application in Foreign Exchange Rates vs. IRR (Iranian Rial) ", [J]. International Journal of Human and Social Sciences,2007,1;3
[45]Mandelbrot B., "Fractals and Scaling in Finance "[M]. New York, USA.Springer,1997: P51-62
[46]Marties A.K., "The Application of Chaos Theory in the Philippine Foreign Exchange Market" [J]. Khanser Publishing House,1999(12)65-68
[47]Michael Bask., "Deteriminsitic Chaos in Exchange Rates?"[J]. Umea Economices Studies, 1998(13):465-470
[48]Michael Bask., "Dimensions, and Lyapunov Exponents From Exchange Rates Series "[J]. Chaos,Solutions and Fractals,1996(12):2199-2214
[49]Michael Bask., "A Positive Lyapunov Exponent in Swedish Exchange Rates? "[J]. Chaos, Solutions and Fractals,2002(14)1295-1304
[50]Meese R A, Rogoff R. "Empirical Exchange Rate Models of the Seventies:Do They Fit Out of Sample "[J]. Journal of International Economics,1983,14:3-24.
[51]Meese R.A. and Rose R.K., "An Empirical Assessment of Nonlinear ties in Models of Exchange Rate Determination "[J]. Review of Economic Studies,1991,(58)603-619
[52]Moshiri S., "Testing for Deterministic Chaos in Futures Crude Oil Price:Does Neural Network Lead to Better Forecast? " Economics, Working Paper.2004.5
[53]Mussa M. "Empirical Regularities in the Behavior of Exchange Rate and Theories of the Foreign Exchange Market" [A]. in:Policies for Employment, Prices, and Exchange Rates[C]. Karl Brunner,Allan H Meltzer. (eds), Carnegie-Rochester Conference Series on Public Policy,1979
[54]ObstfeldM, Rogoff K. "The Six Major Puzzles in International Macroeconomics:Is There A Common Cause" [A]. in:NBER Macroeconomics Annual [C]. Bernanke B, Rogoff K. (eds), CambridgeMA,2000
[55]R.Day and W.Huang, "Bulls,Bear and market sheep" [J] Journal of Economic Behavior and Organization 14(1990),299-329
[56]Richards G., "The Fractal Structure of Exchange Rates:Measurement and Forecasting " [J]. Journal of International Financial Markets,2000(10):163-180
[57]Schwartz, A.,2000. "The rise and the fall of foreign exchange market intervention as a policy tool"[J]. Journal of Financial Services Research 18,319-339.
[58]Schwatz and Yousefi., "On Complex Behavior and Exchange Rates Dynamics " [J]. Chaos, Solution and Fractals,2003(18)503-523
[59]Thomas Gehrig and Lukas Menkhoff, " The Use of Flow Analysis in Foreign Exchange: Exploratory Evidence ",2001
[60]T. Gehrig and L. Menkhoff, "The Use of Flow Analysis in Foreign Exchange:Exploratory Evidence",2001
[61]W.Huang and R.day, "Chaotically switching bear and bull markets:The derivation of stock price distributions from behavioral rules ", Nonliner Dynamic and Evolutionary Economics, Oxford University Press, Oxford,1993, pp.169-182
[62]Weston R. and Permachandran P., "A Chaos Analysis of the New Zealand Exchange Rates 1985-2004" [J]. Emerging Financial Markets and Services Conference,2004(5)261-268
[63]Wieland C., "Controlling Chaos in Higher Dimensional Maps with Constant Feedback:An Analytical Approach". Physical Review,2002(66)58-75
[64]Wieland, C.,2002. "Controlling chaos in higher dimensional maps with constant feedback: an analytical approach " [J].Physical Review E 66,016205,1-8.
[65]Wieland C. and Westerhott F.H., "Exchange Rates Dynamics, Central Bank Interventions and Chaos Control Methods "[J]. Modeling, Computing and mastering Complexity,2003(22):22-26