非线性协整时间序列的非参数方法及其应用研究
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摘要
本文主要研究了非线性协整理论的非参数检验与估计两个领域,包括非线性存在性,混沌与分形特征,非线性非平稳检验以及非线性协整检验与估计。基本梳理清楚了这两个领域的研究脉络和框架。本文运用Gauss编程实现了所提各种非参数检验方法,MC仿真给出了相关统计量的临界值表,并比较了各方法的优劣。在随后的实证研究中,本文对我国货币各变量序列,以及我国与国际股市指数序列应用所给出的非线性协整理论的非参数方法进行了非线性存在性检验,混沌与分形特征检验,存在非线性的非平稳检验以及非线性协整检验与估计,得出了较此前学者们应用线性协整理论相关方法更一般的结论。综合看,本文主要在如下几个方面做了开拓性研究：
第一,较为详细地梳理了线性协整理论的内容,对个中细节进行了注解,使得理论脉络更为清晰明了,从而增进了协整理论的易读性。
第二,对线性加强型神经网络在时间序列的非线性存在性检验中的应用提出了新的方法,即加强型小波神经网络并给出了新的实现算法：改进的带动量的LM算法。MC仿真表明,高斯小波、墨西哥帽小波等两线性加强型小波神经网络方法效果较好。
第三,发现应用小数据量法实现的最大Lyapunov指数值的意义在随机条件下和确定性混沌条件下是不一致的。因此,利用最大Lyapunov指数探讨非线性协整尚需商榷。
第四,发展了秩检验方法,推导了其分布,针对非高斯的单峰分布和存在序列相关性问题提出了相应的改进方法和实现方法,即基于Bootstrap和Block Bootstrap抽样的单位根逆得分秩检验方法。
第五,给出了协整的秩检验方法和记录数检验方法的检验临界值表和响应面函数,并应用上述方法对中国与世界主要证券市场股指进行了实证分析,发现其更多存在的是非线性协整关系。
第六,研究了三种神经网络应用于非线性协整理论的可行性,比较了其优劣,特别地,提出了带动量改进的LM算法的小波神经网络,使得其更具泛化能力。另外,本文还提出应用加强型神经网络对非线性非平稳时间序列进行滤波,其更适用于非线性的情形。
This paper studied two areas of non-parametric testing and estimating methods in nonlinear cointegration theory including non-linear existence, Chaos and Fractal, nonlinear non-stationary test, and nonlinear cointegration test and estimation; clearly distinguished the basic research context and framework. Then realized various non-parametric test methods proposed in this paper by Gauss programming and given the threshold table of related statistics, compared the pros and cons of each methods by MC simulation methods. In this paper, the subsequent empirical study was researched on the variables of currency, China and the international stock market index. Using the non-parametric methods of nonlinear Cointegration theory, the sequence tests was given including testing the existence of nonlinear, the chaotic and fractal characteristics, the nonlinear non-stationary and the nonlinear cointegration, then the estimation of the nonlinear cointegration was discussed. Therefore, got more general conclusion related to linear cointegration theory. Comprehensive view, this paper has done in the following pioneering research:
Firstly, a more detailed sort of linear cointegration theory for the contents was given, some details was Noted, which makes the context more explicit, thus enhanced the accessibility.
Secondly, presented a new method, namely, the enhanced linear wavelet neural network, which in the application of testing the presence of nonlinear time series, and gave a new realization algorithm:the improved momentum LM algorithm. MC simulation showed that the method of Gauss and Mexico Cap WNN had good power.
Thirdly, found that the meaning of maximum Lyapunov index value achieved by the small-data method was inconsistent under conditions of random and deterministic chaos. Therefore, using the maximum Lyapunov index of nonlinear cointegration still needed discussion.
Fourthly, developed the rank test method for non-Gaussian single-peak distribution and the presence of serial correlation, put forward the improved method and implementation method, that is, the Unit Root Inverse-score rank test which based on Bootstrap and Block Bootstrap sampling.
Fifthly, given the threshold table and response surface function of the rank cointegration test and the record counting cointegration Test. And applied those methods in China and the world's major stock market indexes, empirical analysis found that there were more nonlinear cointegration.
Sixthly, the feasibility of three neural network methods applied for nonlinear cointegration was studied, and their advantages and disadvantages were compared. in particular, proposed the wavelet neural network with improved momentum LM algorithm, making it more generalization. In addition, the paper also proposed the application of enhanced neural network for filtering nonlinear non-stationary time series, which was more suitable for nonlinear situations.
第一,较为详细地梳理了线性协整理论的内容,对个中细节进行了注解,使得理论脉络更为清晰明了,从而增进了协整理论的易读性。
第二,对线性加强型神经网络在时间序列的非线性存在性检验中的应用提出了新的方法,即加强型小波神经网络并给出了新的实现算法：改进的带动量的LM算法。MC仿真表明,高斯小波、墨西哥帽小波等两线性加强型小波神经网络方法效果较好。
第三,发现应用小数据量法实现的最大Lyapunov指数值的意义在随机条件下和确定性混沌条件下是不一致的。因此,利用最大Lyapunov指数探讨非线性协整尚需商榷。
第四,发展了秩检验方法,推导了其分布,针对非高斯的单峰分布和存在序列相关性问题提出了相应的改进方法和实现方法,即基于Bootstrap和Block Bootstrap抽样的单位根逆得分秩检验方法。
第五,给出了协整的秩检验方法和记录数检验方法的检验临界值表和响应面函数,并应用上述方法对中国与世界主要证券市场股指进行了实证分析,发现其更多存在的是非线性协整关系。
第六,研究了三种神经网络应用于非线性协整理论的可行性,比较了其优劣,特别地,提出了带动量改进的LM算法的小波神经网络,使得其更具泛化能力。另外,本文还提出应用加强型神经网络对非线性非平稳时间序列进行滤波,其更适用于非线性的情形。
This paper studied two areas of non-parametric testing and estimating methods in nonlinear cointegration theory including non-linear existence, Chaos and Fractal, nonlinear non-stationary test, and nonlinear cointegration test and estimation; clearly distinguished the basic research context and framework. Then realized various non-parametric test methods proposed in this paper by Gauss programming and given the threshold table of related statistics, compared the pros and cons of each methods by MC simulation methods. In this paper, the subsequent empirical study was researched on the variables of currency, China and the international stock market index. Using the non-parametric methods of nonlinear Cointegration theory, the sequence tests was given including testing the existence of nonlinear, the chaotic and fractal characteristics, the nonlinear non-stationary and the nonlinear cointegration, then the estimation of the nonlinear cointegration was discussed. Therefore, got more general conclusion related to linear cointegration theory. Comprehensive view, this paper has done in the following pioneering research:
Firstly, a more detailed sort of linear cointegration theory for the contents was given, some details was Noted, which makes the context more explicit, thus enhanced the accessibility.
Secondly, presented a new method, namely, the enhanced linear wavelet neural network, which in the application of testing the presence of nonlinear time series, and gave a new realization algorithm:the improved momentum LM algorithm. MC simulation showed that the method of Gauss and Mexico Cap WNN had good power.
Thirdly, found that the meaning of maximum Lyapunov index value achieved by the small-data method was inconsistent under conditions of random and deterministic chaos. Therefore, using the maximum Lyapunov index of nonlinear cointegration still needed discussion.
Fourthly, developed the rank test method for non-Gaussian single-peak distribution and the presence of serial correlation, put forward the improved method and implementation method, that is, the Unit Root Inverse-score rank test which based on Bootstrap and Block Bootstrap sampling.
Fifthly, given the threshold table and response surface function of the rank cointegration test and the record counting cointegration Test. And applied those methods in China and the world's major stock market indexes, empirical analysis found that there were more nonlinear cointegration.
Sixthly, the feasibility of three neural network methods applied for nonlinear cointegration was studied, and their advantages and disadvantages were compared. in particular, proposed the wavelet neural network with improved momentum LM algorithm, making it more generalization. In addition, the paper also proposed the application of enhanced neural network for filtering nonlinear non-stationary time series, which was more suitable for nonlinear situations.
引文
[1]Abadir, K.M. and Taylor, A.M.R.(1999). On the definitions of (co-)integration [J]. Journal of Time Series Analysis 20:129-137.
[2]Albano, A. M., et al. (1988).SVD and Grassberger-Procaccia algorithm.Physical Reviews A 38:3017-3026.
[3]Albano, A.M. (1991). Using high-order correlations to define an embedding window [J]. Physica D 54(1):85-97.
[4]Andrews, D. (1966). Note on Higher Order Spectra [J]. Ann.Inst.Statist. Math 18:123-126.
[5]Aparicio, F.M. and A.Escribano (1998). Information-Theoretic Analysis of Serial Dependence and Cointegration[J]. Studies in Nonlinear Dynamics & Econometrics 3:119-140.
[6]Aparicio, F.M., A. Escribano, and A. Garcia(2005). Synchronicity Between Financial Time Series:An Exploratory Analysis. In Progress in Financial Markets Reserch(ed.C.Kystsou). New York Nova Publishers.
[7]Aparicio, F.M., A. Escribano, and A.E. Sipols(2006). Rang Unit-Root (RUR) Test:Robust Against Nonlinearities, Error Distributions, Structural Break and Outliers[J]. Journal of Time Series Analysis 27(4):545-576.
[8]Ashley, R., D. Patterson and M. Hinich (1986). A Diagnostic Test for Nonlinear Serial Dependence in Time Series Fitting Errors [J]. Journal of Time Series Analysis 7:165-178
[9]Balk,N.S. and Fomby,T.B.(1997). Threshold Cointegration[J]. International Economic Review 38:627-645.
[10]Bareau,B., Teliala,I. and Kaisa,S.(1996). Neural Networks and Genetic Algorithms for Bankruptcy Predictions[J].Expert Systems With Applications,1(4):407-413.
[11]Barnett, W.A. and P. Chen(1988). Deterministic Chaos and Fractal Attractors as Tools for Nonparametric Dynamical Inferences [J]. Mathematical Computing and Modelling 10:275-296.
[12]Barron, A.R.(1991). Universal Approximation Bounds for Superpositions of a Sigmoidal Function[R]. Technical Report 58, Department of Statistics, University of Illinis.
[13]Beveridge, Stephen and C.R.Nelson(1981). A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the'Business Cycle'[J]. Journal of Monetary Economics 7:151-174.
[14]Blomqivist, N.(1950).On a Measure of Dependence between two Random Variables[J].Annals of Mathematical Statistics 36:593-600.
[15]Box, G.E.P., and G.M. Jenkins (1970). Time Series Analysis, Forecasting and Control[M]. San Fransisco:Holden Day.
[16]Box, G.E.P, Cox D.R.(1964). An Analysis of Transformations[J]. Journal of the Royal Statistical Society. Series B (Methodological),26(2):211-252.
[17]Breiman,L,& Friedman,J.H.(1985). Estimating Optimal Transformations for Multiple Regression and Correlation[J].JASA,80:580-607.
[18]Breitung J. and C. Gourieroux(1997).Rank tests for unit roots[J], Journal of Econometrics, 81,2-27
[19]Breitung J.(2001).Rank tests for nonlinear cointegration[J]. Journal of Business and Economic Statistics 19:331-40.
[20]Brock,W. A. and E.G Baek(1991). Some Theory of Statistical Inference for Nonlinear Science [J]. Review of Economic Studies 58:697-716.
[21]Broomhead,D.S. and D.Lowe(1988). Multivariable Functional Interpolation and Adaptive Networks[J]. Complex Systems,2(2):321-355.
[22]Burns,A.F. and Mitchell,W.C.(1946). Measuring Business Cycles[M]. Columbia University Press.
[23]Buzug, P.T. (1992). Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors [J]. Physical Reviews A 45(10):7073-7084.
[24]Buzug,P.T. (1992).Comparison of algorithms calculating optimal embedding parameters for delay time coordinates [J]. Physica D 58(2):127-137.
[25]Chen Ping(1988). Empirical and Theoretical Evidence of Monetary Chaos[J]. System Dynamics Review 4:81-108.
[26]Davidson, J.E.H., Hendry, D.F., Srba, F., and S. Yeo(1978). Econometric Modeling of the Aggregate Time Series Relationships between Consumer's Expenditure and Income in the United Kingdom[J]. Economic Journal 88:661-692.
[27]Day,R.H.(1982). Irregular Growth Cycles[J]. American Economic Review 72:406-414.
[28]Day,R.H.(1983). The emergence of chaos from classical economic growth[J]. Quarterly Journal of Economics 5:201-213.
[29]Cover J.P. (1992).Asymmetric Effects of Positive and Negative Money Supply Shocks[J]. Quarterly Journal of Economics,107 (4):1261-1281.
[30]Cox,D. D.(1983). A symptotics for M-type smoothing splines[J]. Annals of Statistics 11:530-551.
[31]Cutler, C.(1991). Some Results on the Behavior and Estimation of the Fractal Dimensions of Distributions on Attractors [J]. Journal of Statistical Physics 62:651-708.
[32]Cybenko,G.(1989). Approximation by Superpositions of a Sigmoidal Function[J]. Mathematics of Control, Signals and Systems 2:303-314.
[33]Denker, G. and K.G. eller (1986). Rigorous Statistical Procedure for Data from Dynamical Systems[J]. Journal of Statistical Physics 44:67-93.
[34]Dornbusch,R.(1976). Expectation and exchange rate dynamics[J]. Journal of Political Economy 84:1161-76.
[35]Dufrenot,G., Mathieu,L. and V.Mignon(2000).Pourquoi les taux de change d'equilibre deveintils de leur valuer fundamentale? Une analyse par la cointegration non-lineaire[C]. Communication at the International Congress on Reconstruire I'architecture du systeme monetaire international, Sienna,Italy.
[36]Dufrenot,G.,Valerie Mignon(2002). Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance[M]. Kluwer Academic Publishers.
[37]Dumas,B.(1992).Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World[J]. Review of Financial Studies 2:153-180.
[38]Duolao Wang and Michae(2004). Murphy Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm[J]. Journal of Data Science 2:329-346.
[39]Efron Bradley(1979). Bootstrap methods:another look at the jackknife [J]. The Annals of Statistics 7(1):1-26.
[40]Ehud,D.Karninl(1990). A simple procedure for pruning back-propagation trained neural network[J].IEEE Trans on Neural Networks 1(2):239-242.
[41]Embrechts,P., C. Kluppelberg and T.Mikosch(1999). Modeling Extremal Events (for Insurance and Finance)[M]. Springer-Werlag, Heidelberg.
[42]Engle,R.F. and C.WJ.Granger(1987). Cointegration and Error Correction:Represention, Estimation and Testing. Econometrica 55:251-276.
[43]Erdogan,S.S.,Geok-See.Ng and P.K.-H.Chan(1996). Measurement Criteria for Neural Network Pruning[C].IEEE Region 10 Annual Conference:83-89.
[44]Escribano A., A.E. Sipols and F.M.Aparicio(2006). Nonlinear Cointegration and Nonlinear Error Correction:Record Counting Cointegration Tests. Communications in Statistics[J]. Simulation and Computation 35(4):939-956.
[45]Fahlman, S.E. and C.Lebiere(1990).The cascade-correlation learning architecture[J]. Advances in Neural Information Processing Systems 2:524-532.
[46]Fama,E.(1965). The Behavior of Stock Market Prices[J].Journal of Business,38:34-106.
[47]Feigenbaum,M.J.(1978). Quantitative Universality for a Class of Nonlinear Transformations[J]. Journal of Statistical Physics 19:25-52.
[48]Feigenbaum,M.J.(1979). The Onset Spectrum of Turbulence[J]. Physical Letters A 74:375.
[49]Feigenbaum,M.J.(1980). The Transition to Aperiodic Behaviour in Turbulent Systems[J]. Commun. Math. Physics.77:65.
[50]Fraser,A.M. (1989). Information and entropy in strange attractors[J]. IEEE Trans on IT Mar 35(2):245-262.
[51]Friedman,M.(1988) Money and the Stock Market[J]. Journal of Political Economy,,96 (2): 221-245.
[52]Gilmore, C.G. (1993). A New Test for Chaos [J]. Journal of Economic Behavior and Organization 22:219-237.
[53]Goldberg,D.E.(1989). Genetic Algorithms:In Search Optimization & Machine Learning[M]. Massachusetts,USA:Addison-wesley Publishing Company.
[54]Granger, C.W.J(1981).Some Properties of Time Series Data and Their Use in Econometric Model Specification [J]. Journal of Econometrics 23:121-130.
[55]Granger, C.W.J. and Weiss, A.A(1983).Time Series Analysis of Error-correction Models, in: Studies in Econometrics, Time Series, and Multivariate Analysis (Academic Press, New York): 255-278.
[56]Granger, C.W.J(1986).Developments in the Study of Cointegrated Economic Variables[J]. Oxford Bulletin of Economics and Statistics 48:213-228.
[57]Granger, C.W.J.(1995). Modelling Nonlinear Relationships Between Extended-Memory Variables[J]. Economica,63:265-279.
[58]Granger, C.W.J and Namwon Hyung (2004). Occasional Structural Breaks and long Memory with an Application to the S&P 500 Absolute Stock Returns[J]. Journal of Empirical Finance 11:399-421.
[59]Grassberger, P. and I. Procaccia (1983). Estimation of the Kolmogorov entropy from a chaotic signal[J]. Physical Reviews A 28:2591-2593.
[60]Grassberger, P. and I. Procaccia (1983). Measuring the Strangeness of Strange Atrractors [J]. Physica 9D:189-208.
[61]Halsty, T.C., M.H. Jensen and L.P. Kadanoff. (1986). Fractal Measures and Their Singularities:The Characterization of Strange Sets[J]. Physical Reviews A 33:1141.
[62]Hamilton,&James D. Time Series Analysis[M]. Princeton University Press,1994.
[63]Hannan, E.J. (1982). The Estimation of the Order of an ARMA Process[J]. Annals of Statistics 8:1071-1081.
[64]Hansen and E.Bruce(1992). Efficient Estimation and Testing of Cointegrating Vectors in the Presence of Deterministic Trends[J]. Journal of Econometrics 53:87-121.
[654]Hardle,W., Lutkepohl, H. and Chen,R. (1997). A Review of Nonparametric Time Series Analysis[J]. International Statistical Review 65:49-72.
[66]Masry, E. and Fan, J.(1997). Local Polynomial Estimation of Regression Functions for Mixing Processes[J]. Scandinavian Journal of Statistics 24:165-179.
[67]Hendry, D.F., and G.E. Mizon (1978). Serial Correlation as a Convenient Simplification Not a Nuisance:a Comment on a Study of the Demand for Money by the Bank of England[J]. Economic Journal 88:549-563.
[68]Hesieh,D. (1989). Testing for Nonlinear Dependence in Daily Foreign Exchange Rates[J]. Journal of Business 62(3):339-359.
[69]Hinich, M.J.(1982). Testing for Gaussianity and Linearity of a Stationary Time Series [J]. Journal of Time Series Analysis 3:169-176.
[70]Holger Kantz, and Thomas Schreiber. Nonlinear Time Series Analysis[M](影印版).清华大学出版社,北京：2000.
[71]Holland,J.H.(1975). Adaptationin Natural and Artificial Systems[M].Boston,USA:MIT Press.
[72]Hornik, K., Stinchcombe,M. and H. White(1989). Multi-layer Feedforward Networks are Universal Appromiximators[J]. Neural Networks 2:359-366.
[73]Hurst, H. (1951). Long Term Storage Capacity of Reservoirs [J]. Transactions of the American Society of Civil Engineers 116:770-799.
[74]Johansen, S.(1988). Statistic Analysis of Cointegration Vectors[J]. Journal of Economic Dynamics and Control 12:231-254.
[75]Johansen, S.(1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models[J]. Econometrica 59(6):1551-1580.
[76]Kah Phooi Seng, Zhihong Man, Hong Ren Wu.(2002). Lyapunov-theory-based Radial Basis Function Networks for Adaptive Filtering[J].IEEE Transactions on Circuits and Systems. 49(8):1215-1220.
[77]Kantz,H. (1994). A Robust Method to Estimate the Maximal Lyapunov Exponent of a Time Series[J]. Physics letters. A 185:11,77-87.
[78]Kantz, H.and T.Schreiber(1997). Nonlinear Time Series Analysis[M]. Cambridge:Cambridge Univ.Press.
[79]Karras, G. (1996).Are the Output Effects of Monetary Policy Asymmetric? Evidence from a Sample of European Countries[J].Qxford Bulletin of Economics and Statistics,58:267-278.
[80]Karras, G. and H.Stokes(1999).Are the Output Effects of Money-supply Shock Asymmetric? Evidence from Prices, Consumption and Investment[J], Journal of Macroeconomics 21:713-728.
[81]Keenman, D.M. (1985). A Turkey Non-additivity-type Test for Time Series Nonlinearity [J]. Biometrika,72:39-44.
[82]Kember, G.,and A.C. Fowler (1993). A correlation function for choosing time delays in phase portrait reconstructions [J]. Physical Letters A 179(2):72-80.
[83]Keynes, J.M.(1936). The General Theory of Employment, Interest and Money[M]. London: Macmillan Cambridge University Press.
[84]Kim, H.S., R. J. Eykholt and D. Salas (1999). Nonlinear dynamics, delay times, and embedding windows [J].Physica D 127 (1):48-60.
[85]Kodres L.E.,Papell D.H.(1991). Nonlinear dynamics in foreign exchange futures market[R]. Working paper, Universtiy of Michigan.
[86]Kuan, C.M. and H. White(1990). Predicting Appliance Ownership Using Logit, Nueral Networks and Regression Tree Models[R]. BEBR Working Paper 90-1647.
[87]Kuan, C.M. and T. Liu(1995). Forcasting Exchange Rate Using Feedforward and Recurrent Nueral Networks[J]. Journal of Applied Econometrics 10:347-364.
[88]Kugiumtzis, D.(1996). State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length [J]. Physica D 95(1):13-28.
[89]Kwiathowski, D. and P.C.B. Phillips, P. Schmidt and Y. Shin(1992). Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root:How sure are We that Economic
[90]Time Series have a Unit Root? [J]. Journal of Econometrics 54:159-178.
[91]Kyung-Joong Kim,Sung-Bae Cho(2008).Evolutionary ensemble of diverse artificial neural networks using speciation[J]. Neurocomputing.71:1604-1618.
[92]Lee, D. and P. Schmidt(1996). On the Power of the KPSS Test of Stationarity Against Fractionally-integrated Alternatives[J]. Journal of Econometrics 73:285-302.
[93]Lee,T,-H., H.White and C.W.J Granger(1993). Testing for Neglected Nonlinearity in Time Series Models:A Comparison of Neural Network Methods and Alternative Tests [J]. Journal of Econometrics 56:269-290.
[94]Lei Xu(1993). Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, And Curve Detection[J]. IEEE Transaction on Neural Networks,4(4):636-649.
[95]Lindgren,G. and H. Rootzen(1987). Extremal Values:Theory and Technical Applications[J]. Scandinavian Journal of Statistics 14:241-279.
[96]Liu,T., C.W.J Granger and W. Heller (1992). Using the Correlation Exponent to Decide if an Economic Series is Chaotic[J]. Journal of Applied Econometrics 7S:525-540.
[97]Lo, A.W. (1991). Long-Term Memory in Stock Market Prices [J]. Econometrica 59:1279-1313.
[98]Mandelbrot, B.B.,and M.Taqqu (1979). Robust R/S Analysis of Long Run Serial Correlation. Bulletin of International Statistical Institute 48, Book 3:59-104.
[99]Mankiw,G.N.(1991)The reincarnation ofKeynesian economics[J],NBER Working Paper No.3885.
[100]Mantalos, P.(2000). A Graphical Investigation of the Size and Power of the Grange-Causality Tests inlntegrated-Cointegrated VAR Systems[J], Studies in Non-linear Dynamics and Econometrics 4:17-33.
[101]Martin T.Hagan, Howard B.Demuth and Mark H.Beale著.戴葵等译.神经网络设计[M].北 京：机械工业出版社,2002.
[102]Mitchell,W.C.(1927). Business Cycles:The Problem and its Setting[M]. New York,:National Bureau of Economic Research.
[103]Mcleod, A.I. and W.K. Li (1983). Diagnostic Checking ARMA Time Series Models Using Squared Residual Autocorrelations [J]. Journal of Time Series Analysis 4:169-176.
[104]Moody, J. and C.Darken(1988). Learning with Localized Receptive Fields[C]. In Sejnowski T, Touretzky D, Hinton G, editors, Connectionist Models Summer School, Carnegie Mellon University.
[105]Moody, J.(1994).Prediction risk and architecture selection for neural networks[C].Statistics to Neural Networks:Theory and Pattern Recognition Applications, NATO ASI Series F. New York:178-197.
[106]Mundell,R.A. (1963)Capital mobility and stabilization policy under fixed and flexible exchange rates[J], Canadian Journal of Economics and Political Science,29,475-85
[107]Neftci,S.N.(1984). Are Economic Time Series Asymmetric over the Business Cycles?[J]. Journal of Political Economy,92:301-328.
[108]Packard, N.H., J. P. Crutchfield and J.D. Farmer, et al. (1980). Geometry from a Time Series [J]. Physical Review Letter 45(3):712-716.
[109]Parzen, E. (1962). On Estimation of a Probability Density Function and Mode [J], Annual Math Statistics 33:1065-1076.
[110]Peters, E.E(1991).Chaos and Order in the Capital Markets-a new View of Cycles, Prices and Market Volatility[M]. New York:John Wiley&Sons, Inc.
[111]Peters E.E.(1994). Fractal Market Analysis:Applying Chaos Theory to Investment and Economics[M]. New York:John Wiley & son Inc.
[112]Peters E.E.(1996).Chaos and Order in the Capital Market. Second Ed[M],John Wiley& Sons press.
[113]Philippatos, G.C., Pilarinu,E. and Malliaris, A.G.(1994). Chaotic Behavior in Prices of European Equity Markets:A Comparative Analysis of Major Economic Regions[J]. Journal of Multinational Finance Managemen,3:5-24.
[114]Ramsey, J.B(1969).Tests for Specification Errors in Classical Linear Least Squares Regression Analysis[J]. Journal of the Royal Statistical Society B 31:350-371.
[115]Ramsey, J. and H. Yuan (1989). Bias and Error Bias in Dimension Calculation and their Evaluation in some Simple Models [J]. Physical Letters A 134:287-297.
[116]Richards,G.R.(2000).The Fractal Structure of Exchange Rates:Measurement and Forecasting[J] Journal of International Financial Markets, Institutions and Money.10:163-180.
[117]Rosenstein M.T., J.J. Collins and L.C.De (1993), A Practical Method for Calculating Largest lyapunov Exponents from Small Data Sets [J]. Physica D 65:117-134.
[118]Rosenstein, M.T., J.J.Collins and C.J.De Luca (1994). Reconstruction expansion as a geometry-based framework for choosing proper delay times [J]. Physica D 73(1):82-98.
[119]Ruppert D, M.P.Wand.(1994). Multivariate locally weighted least squares regression[J]. Annals of Statistics 22:1346-1370.
[120]Sato, S., M. Sano, and Y. Sawada (1987). Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in high Dimensional Chaotic Systems [J]. Progress of Theoretical Physics 77:1-5.
[121]Scheinkman, J. and B. Lebanon (1989). Nonlinear Dynamics and Stock Returns [J]. Journal of Business 62:311-337.
[122]Schmidt, P. and P.C.B.Phillips (1992). LM test for a unit root in the presence of deterministic trends[J]. Oxford Bulletin of Economics and Statistics 54,257-287.
[123]Sercu, P., Uppal, R. and C.Van Hulle(1995). The Exchange Rate in the Presence of Transaction Costs:Implications for Tests of Purchasing Power Parity[J]. Journal of Finance 50:1309-1319.
[124]Smith, R.L. (1992). Estimating Dimension in Noisy Chaotic Time Series [J]. Journal of Royal Statistical Society B 54:329-352.
[125]Sowell,F.B.(1990).The fractional unit root distribution[J]. Economica 58:495-505. Srinivas,M. and L.M.Patnaik (1996). Genetic Search:Analysis Using Fitness Moments[J]. IEEE Transactions on Knowledge and Data Engineering 8(1):120-133.
[126]Stutzer, M,J.(1980). Chaotic Dynamics and Bifurcations in a Macro Model[J]. Journal of Economic Dynamics and Control 4(3):353-376.
[127]Taqqu,M.S.,V.Teverosky and W.Willinger(1995). Estimations for long-range dependence:an empirical study[J]. Fractals 3(4):765-788.
[128]Takens, F. (1981). Detecting Strange Attractor in Turbulence. in Dynamical systems and turbulence, Warwich,1980, Lecture Notes in Mathe-matics, Rand and Young eds 898: 366-381.
[129]Tj(?)stheim,D.(1994). Non-linear Time Series:a selective Review[J]. Scandinavian Journal ofStatistics 21:97-130.
[130]Tong,H.(1990). Non-linear Time Series:A Dynamical Systems Approach[M]. Oxford University Press, Oxford.
[131]Tong,H. (1995). A personal overview of non-linear time series analysis from a chaos perspective(with discussion)[J]. Scandinavian Journal of Statistics 22:399-445.
[132]Tsay, R.S.(1986). Nonlinearity Test for Time Series [J]. Biometrika 73:461-466.
[133]Tsay,R..S(2002). Analysis of Finacial Times Series[M]. John Wiley&Sons,Inc,New York.
[134]Vance L. Martin and Kim Sawyer (1994), Statistic techniques for modeling nonlinearities. In John Creedy, Vance L. Martin(ed.), Chaos and nonlinear models in economics:theory and applications. Edward Elgar Publishing Company:113-134.
[135]White, H.(1988). Economic Prediction Using Nueral Networks:The Case of IBM Stock Prices[C]. Proceedings of the IEEE Second International Conference on Neural Networks 2:451-458.
[136]White, H.(1989). Some Asymptotic Results for Learning in Single Hidden-layer Feedforward Network Models[J]. Journal of the American Statistical Association 84:1003-1013.
[137]Wolf A., J.B. Swift, H.L. Swinney and J.A. Vastano (1985). Determining Lyapunov exponents from a time series [J]. Physica D 16:285-317.
[138]Xiao-Ming Li.(2006). A Revisit Of International Stock Market Linkages:New Evidence From Rank Tests For Nonlinear Cointegration[J]. Scottish Journal of Political Economy 2:174-197.
[139]Yao,Q. and Tong,H.(1995a). On Initial-condition Sensitivity and Prediction in Nonlinear Stochastic Systems[J]. Bull. Int. Statist. Inst.50:395-412.
[140]Yao,Q. and Tong,H.(1995b). On Prediction and Chaos in Stochastic Systems[J]. Philosophical transactions A:mathematical, physical and engineering sciences,348 (1688):357-369.
[141]Yule, G.U.(1927). On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunsport Numbers[J]. Philosophical Transactions 226A:267-298.
[142]Zhang Qinghua, Benveniste, A. (1992). Wavelet Networks[J]. IEEE Transactions on Neural Networks 3(6):888-898.
[143]陈守东,韩广哲,荆伟.主要股票市场指数与我国股票市场指数间的协整分析[J].数量经济技术经济研究,2003(5)：124-129.
[144]陈小平,赵鹤鸣,杨新艳.遗传前馈神经网络在函数逼近中的应用[J].计算机工程.2008,34(20)24-28.
[145]储海林,吕小宁,李哲.分形与统计学[J].统计研究,2004(2)：35-37.
[146]郑湄,苗佳.应用协整检验对中国股市及美、英股市联动关系的分析[J].山东社会科学,2004(12)：113-115.
[147]范剑青,姚琦伟著.陈敏译.非线性时间序列-建模,预报及应用[M].高等教育出版社,2005.
[148]韩非,肖辉.中美股市间的联动性分析[J],金融研究,2005(11)：117-129
[149]黄忠明,吴志红,刘全喜.几种用于非线性函数逼近的神经网络方法研究[J].兵工自动化.2009,28(10)：88-92.
[150]黄建国,罗航,王厚军,龙兵.运用GA-BP神经网络研究时间序列的预测[J].电子科技大学学报.2009,38(5)：687-692.
[151]冯今朝,王仲生.基于LM优化算法的神经网络在航空发动机转子故障诊断中的应用[J].宇航计测技术.2007,27(2)：18-21,49.
[152]梁勇,孟桥,陆佶人.Lyapunov指数的算法改进与加权预测[J].声学技术,2006,(05)：463-467.
[153]雷钦礼.非线性协整模型：理论与方法[J].统计研究,2009(3)：81-91.
[154]林文夫著,冉启康,朱保华译.计量经济学.上海财经济大学.2005.10.
[155]林嘉宇,王跃科,黄芝平,等.语音信号相空间重构中时间延迟的选择—复自相关法[J].信号处理,1999,15(3)：220-225.
[156]罗伯特S.平狄克&丹尼尔L.鲁宾费尔德著.钱小平等译.计量经济模型与经济预测(第4版)机械工业出版社1999.11.
[157]刘汉中,傅元海.基于残差的非对称单位根自助法检验研究[J].数量经济技术经济研究,2008(8)：151-160.
[158]李春鑫,李天伟,王孝通.基于小波模糊网络的非线性函数逼近方法的研究[J].计算机测量与控制.2006,14(3)：322-323,338.
[159]李明国,郁文贤.神经网络的函数逼近理论[J].国防科技大学学报,1998,20(4)：70-76.
[160]李洋.小波过程神经网络相关理论及其应用研究[D].博士论文.哈尔滨工业大学,2008.
[161]李美洲.门限及分数维分析及其在经济中的应用[D].博士论文.暨南大学,2008.
[162]李选举.Box-Cox变换及其在MathCAD上的实现[J].数量经济技术经济研究,2000,4：42-44.
[163]乔俊飞,张颖.一种多层前馈神经网络的快速修剪算法[J].智能系统学报.2008,3(2)：173-176.
[164]活尔特.恩德斯(Walter Enders)著.杜江谢志超译.应用计量经济学：时间序列分析(第二版)[M].高等教育出版社.2006.6.
[165]L.沃塞曼[美]著,吴喜之译.现代非参数统计[M].科学出版社.北京：2008.
[166]王国松,杨扬.国际资本流动下我国货币需求函数稳定性检验[J].财经研究,2006(10)：17-25.
[167]王少平.单位根和协整及其结构突变的理论与应用研究(清华大学博士论文)2002.
[168]王忠玉.混沌的计量经济学简评[J].统计研究,2000(2)：61.
[169]王春玲.基于径向基函数网络的非线性系统自适应逆控制[D].硕士论文,山东大学,2007.
[170]施锡铨,艾克凤.股票市场风险的多重分形分形[J].统计研究,2004(9)：33-36.
[171]石建民.股票市场、货币需求与总量经济：一般均衡分析[J].经济研究,2001(5)：45-52.
[172]舒晓惠,雷钦礼,宋金奇.单位根的秩检验及其应用研究[J].统计研究,2009(9)：101-107.
[173]舒晓惠,雷钦礼,陈一非.中国与国际股市的协整分析——基于一种新的非线性协整秩检验方法[J].山西财经大学学报,2010(1)：17-29.
[174]孙青华,张世英.长记忆向量时间序列的非线性协整关系研究[J].天津大学学报,200235(3)：327-331.
[175]田旭光,宋彤,刘宇新.结合遗传算法优化BP神经网络的结构和参数[J].计算机应用与软件,2004,21(6)：69-71.
[176]谢益辉,朱钰.Bootstrap方法的历史发展和前沿研究[J].统计与信息论坛,2008(2)：90-96.
[177]杨庆,秦伟良.R／S和修正R／S方法的实证分析[J].统计与决策,2003(11)：18-19.
[178]杨建刚.人工神经网络实用教程[M].杭州：浙江大学出版社,2001.
[179]杨国为,王守觉,闫庆旭.分式线性神经网络及其非线性逼近能力研究[J].计算机学报.2007,30(2)：189-199.
[180]叶阿忠.非参数经济学[M].南开大学出版,天津：2003.7.
[181]叶阿忠.非线性协整的非参数检验方法[J].预测,2001(1)：79-80.
[182]易行健.关于中国股票市场对货币需求总量与结构影响的分析[J],经济科学,2004
[183]易行健.经济开放条件下的货币需求函数：中国的经验[J],世界经济,2006(4)：49-59.
[184]俞世典,陈守东,黄立华.主要股票指数的联动分析[J].统计研究,2001(8)：42-46.
[185]张世英樊智.协整理论与波动模型.清华大学出版社.2004.
[186]张贤达(1996).时间序列分析—高阶统计量方法[M].北京：清华大学出版社：31-45.
[187]张丹,于朝民,付永杰.基于人工神经网络的传感器非线性拟合方法的研究[J].工业计量.2004,14(5)：31-33.
[188]张喜彬,张世英.关于单整时间序列非线性变换的研究[J].系统工程学报.1998,13(2)：70-77.
[189]张昭昭,沈学利,乔俊飞.基于权值e指数信息熵的前馈网络修剪算法[J].辽宁工程技术大学学报(自然科学版).2009,28(3)：439-441.
[190]钟登华.非线性随机最佳变换模型及其应用[J].系统工程学报.1996,11(3)：84-89.
[191]赵贵兵,石炎福,段文锋,余华瑞.从混沌时间序列同时计算关联维和Kolmogorov熵[J].计算物理,1999,15(3)：309-315.
[192]张尧庭.关于度量变量之间的相关程度[J].上海财经大学学报,1999(12)：60-63.
[193]周建(2005).时间序列建模中滞后阶数选取准则函数的检测效力及其特征[J].系统工程理论与实践,2005年第11期：20-27.
[194]中国人民银行研究局课题组,中国股票市场发展与货币政策完善[J],金融研究,2002(4)：1-12.
[2]Albano, A. M., et al. (1988).SVD and Grassberger-Procaccia algorithm.Physical Reviews A 38:3017-3026.
[3]Albano, A.M. (1991). Using high-order correlations to define an embedding window [J]. Physica D 54(1):85-97.
[4]Andrews, D. (1966). Note on Higher Order Spectra [J]. Ann.Inst.Statist. Math 18:123-126.
[5]Aparicio, F.M. and A.Escribano (1998). Information-Theoretic Analysis of Serial Dependence and Cointegration[J]. Studies in Nonlinear Dynamics & Econometrics 3:119-140.
[6]Aparicio, F.M., A. Escribano, and A. Garcia(2005). Synchronicity Between Financial Time Series:An Exploratory Analysis. In Progress in Financial Markets Reserch(ed.C.Kystsou). New York Nova Publishers.
[7]Aparicio, F.M., A. Escribano, and A.E. Sipols(2006). Rang Unit-Root (RUR) Test:Robust Against Nonlinearities, Error Distributions, Structural Break and Outliers[J]. Journal of Time Series Analysis 27(4):545-576.
[8]Ashley, R., D. Patterson and M. Hinich (1986). A Diagnostic Test for Nonlinear Serial Dependence in Time Series Fitting Errors [J]. Journal of Time Series Analysis 7:165-178
[9]Balk,N.S. and Fomby,T.B.(1997). Threshold Cointegration[J]. International Economic Review 38:627-645.
[10]Bareau,B., Teliala,I. and Kaisa,S.(1996). Neural Networks and Genetic Algorithms for Bankruptcy Predictions[J].Expert Systems With Applications,1(4):407-413.
[11]Barnett, W.A. and P. Chen(1988). Deterministic Chaos and Fractal Attractors as Tools for Nonparametric Dynamical Inferences [J]. Mathematical Computing and Modelling 10:275-296.
[12]Barron, A.R.(1991). Universal Approximation Bounds for Superpositions of a Sigmoidal Function[R]. Technical Report 58, Department of Statistics, University of Illinis.
[13]Beveridge, Stephen and C.R.Nelson(1981). A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the'Business Cycle'[J]. Journal of Monetary Economics 7:151-174.
[14]Blomqivist, N.(1950).On a Measure of Dependence between two Random Variables[J].Annals of Mathematical Statistics 36:593-600.
[15]Box, G.E.P., and G.M. Jenkins (1970). Time Series Analysis, Forecasting and Control[M]. San Fransisco:Holden Day.
[16]Box, G.E.P, Cox D.R.(1964). An Analysis of Transformations[J]. Journal of the Royal Statistical Society. Series B (Methodological),26(2):211-252.
[17]Breiman,L,& Friedman,J.H.(1985). Estimating Optimal Transformations for Multiple Regression and Correlation[J].JASA,80:580-607.
[18]Breitung J. and C. Gourieroux(1997).Rank tests for unit roots[J], Journal of Econometrics, 81,2-27
[19]Breitung J.(2001).Rank tests for nonlinear cointegration[J]. Journal of Business and Economic Statistics 19:331-40.
[20]Brock,W. A. and E.G Baek(1991). Some Theory of Statistical Inference for Nonlinear Science [J]. Review of Economic Studies 58:697-716.
[21]Broomhead,D.S. and D.Lowe(1988). Multivariable Functional Interpolation and Adaptive Networks[J]. Complex Systems,2(2):321-355.
[22]Burns,A.F. and Mitchell,W.C.(1946). Measuring Business Cycles[M]. Columbia University Press.
[23]Buzug, P.T. (1992). Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors [J]. Physical Reviews A 45(10):7073-7084.
[24]Buzug,P.T. (1992).Comparison of algorithms calculating optimal embedding parameters for delay time coordinates [J]. Physica D 58(2):127-137.
[25]Chen Ping(1988). Empirical and Theoretical Evidence of Monetary Chaos[J]. System Dynamics Review 4:81-108.
[26]Davidson, J.E.H., Hendry, D.F., Srba, F., and S. Yeo(1978). Econometric Modeling of the Aggregate Time Series Relationships between Consumer's Expenditure and Income in the United Kingdom[J]. Economic Journal 88:661-692.
[27]Day,R.H.(1982). Irregular Growth Cycles[J]. American Economic Review 72:406-414.
[28]Day,R.H.(1983). The emergence of chaos from classical economic growth[J]. Quarterly Journal of Economics 5:201-213.
[29]Cover J.P. (1992).Asymmetric Effects of Positive and Negative Money Supply Shocks[J]. Quarterly Journal of Economics,107 (4):1261-1281.
[30]Cox,D. D.(1983). A symptotics for M-type smoothing splines[J]. Annals of Statistics 11:530-551.
[31]Cutler, C.(1991). Some Results on the Behavior and Estimation of the Fractal Dimensions of Distributions on Attractors [J]. Journal of Statistical Physics 62:651-708.
[32]Cybenko,G.(1989). Approximation by Superpositions of a Sigmoidal Function[J]. Mathematics of Control, Signals and Systems 2:303-314.
[33]Denker, G. and K.G. eller (1986). Rigorous Statistical Procedure for Data from Dynamical Systems[J]. Journal of Statistical Physics 44:67-93.
[34]Dornbusch,R.(1976). Expectation and exchange rate dynamics[J]. Journal of Political Economy 84:1161-76.
[35]Dufrenot,G., Mathieu,L. and V.Mignon(2000).Pourquoi les taux de change d'equilibre deveintils de leur valuer fundamentale? Une analyse par la cointegration non-lineaire[C]. Communication at the International Congress on Reconstruire I'architecture du systeme monetaire international, Sienna,Italy.
[36]Dufrenot,G.,Valerie Mignon(2002). Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance[M]. Kluwer Academic Publishers.
[37]Dumas,B.(1992).Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World[J]. Review of Financial Studies 2:153-180.
[38]Duolao Wang and Michae(2004). Murphy Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm[J]. Journal of Data Science 2:329-346.
[39]Efron Bradley(1979). Bootstrap methods:another look at the jackknife [J]. The Annals of Statistics 7(1):1-26.
[40]Ehud,D.Karninl(1990). A simple procedure for pruning back-propagation trained neural network[J].IEEE Trans on Neural Networks 1(2):239-242.
[41]Embrechts,P., C. Kluppelberg and T.Mikosch(1999). Modeling Extremal Events (for Insurance and Finance)[M]. Springer-Werlag, Heidelberg.
[42]Engle,R.F. and C.WJ.Granger(1987). Cointegration and Error Correction:Represention, Estimation and Testing. Econometrica 55:251-276.
[43]Erdogan,S.S.,Geok-See.Ng and P.K.-H.Chan(1996). Measurement Criteria for Neural Network Pruning[C].IEEE Region 10 Annual Conference:83-89.
[44]Escribano A., A.E. Sipols and F.M.Aparicio(2006). Nonlinear Cointegration and Nonlinear Error Correction:Record Counting Cointegration Tests. Communications in Statistics[J]. Simulation and Computation 35(4):939-956.
[45]Fahlman, S.E. and C.Lebiere(1990).The cascade-correlation learning architecture[J]. Advances in Neural Information Processing Systems 2:524-532.
[46]Fama,E.(1965). The Behavior of Stock Market Prices[J].Journal of Business,38:34-106.
[47]Feigenbaum,M.J.(1978). Quantitative Universality for a Class of Nonlinear Transformations[J]. Journal of Statistical Physics 19:25-52.
[48]Feigenbaum,M.J.(1979). The Onset Spectrum of Turbulence[J]. Physical Letters A 74:375.
[49]Feigenbaum,M.J.(1980). The Transition to Aperiodic Behaviour in Turbulent Systems[J]. Commun. Math. Physics.77:65.
[50]Fraser,A.M. (1989). Information and entropy in strange attractors[J]. IEEE Trans on IT Mar 35(2):245-262.
[51]Friedman,M.(1988) Money and the Stock Market[J]. Journal of Political Economy,,96 (2): 221-245.
[52]Gilmore, C.G. (1993). A New Test for Chaos [J]. Journal of Economic Behavior and Organization 22:219-237.
[53]Goldberg,D.E.(1989). Genetic Algorithms:In Search Optimization & Machine Learning[M]. Massachusetts,USA:Addison-wesley Publishing Company.
[54]Granger, C.W.J(1981).Some Properties of Time Series Data and Their Use in Econometric Model Specification [J]. Journal of Econometrics 23:121-130.
[55]Granger, C.W.J. and Weiss, A.A(1983).Time Series Analysis of Error-correction Models, in: Studies in Econometrics, Time Series, and Multivariate Analysis (Academic Press, New York): 255-278.
[56]Granger, C.W.J(1986).Developments in the Study of Cointegrated Economic Variables[J]. Oxford Bulletin of Economics and Statistics 48:213-228.
[57]Granger, C.W.J.(1995). Modelling Nonlinear Relationships Between Extended-Memory Variables[J]. Economica,63:265-279.
[58]Granger, C.W.J and Namwon Hyung (2004). Occasional Structural Breaks and long Memory with an Application to the S&P 500 Absolute Stock Returns[J]. Journal of Empirical Finance 11:399-421.
[59]Grassberger, P. and I. Procaccia (1983). Estimation of the Kolmogorov entropy from a chaotic signal[J]. Physical Reviews A 28:2591-2593.
[60]Grassberger, P. and I. Procaccia (1983). Measuring the Strangeness of Strange Atrractors [J]. Physica 9D:189-208.
[61]Halsty, T.C., M.H. Jensen and L.P. Kadanoff. (1986). Fractal Measures and Their Singularities:The Characterization of Strange Sets[J]. Physical Reviews A 33:1141.
[62]Hamilton,&James D. Time Series Analysis[M]. Princeton University Press,1994.
[63]Hannan, E.J. (1982). The Estimation of the Order of an ARMA Process[J]. Annals of Statistics 8:1071-1081.
[64]Hansen and E.Bruce(1992). Efficient Estimation and Testing of Cointegrating Vectors in the Presence of Deterministic Trends[J]. Journal of Econometrics 53:87-121.
[654]Hardle,W., Lutkepohl, H. and Chen,R. (1997). A Review of Nonparametric Time Series Analysis[J]. International Statistical Review 65:49-72.
[66]Masry, E. and Fan, J.(1997). Local Polynomial Estimation of Regression Functions for Mixing Processes[J]. Scandinavian Journal of Statistics 24:165-179.
[67]Hendry, D.F., and G.E. Mizon (1978). Serial Correlation as a Convenient Simplification Not a Nuisance:a Comment on a Study of the Demand for Money by the Bank of England[J]. Economic Journal 88:549-563.
[68]Hesieh,D. (1989). Testing for Nonlinear Dependence in Daily Foreign Exchange Rates[J]. Journal of Business 62(3):339-359.
[69]Hinich, M.J.(1982). Testing for Gaussianity and Linearity of a Stationary Time Series [J]. Journal of Time Series Analysis 3:169-176.
[70]Holger Kantz, and Thomas Schreiber. Nonlinear Time Series Analysis[M](影印版).清华大学出版社,北京：2000.
[71]Holland,J.H.(1975). Adaptationin Natural and Artificial Systems[M].Boston,USA:MIT Press.
[72]Hornik, K., Stinchcombe,M. and H. White(1989). Multi-layer Feedforward Networks are Universal Appromiximators[J]. Neural Networks 2:359-366.
[73]Hurst, H. (1951). Long Term Storage Capacity of Reservoirs [J]. Transactions of the American Society of Civil Engineers 116:770-799.
[74]Johansen, S.(1988). Statistic Analysis of Cointegration Vectors[J]. Journal of Economic Dynamics and Control 12:231-254.
[75]Johansen, S.(1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models[J]. Econometrica 59(6):1551-1580.
[76]Kah Phooi Seng, Zhihong Man, Hong Ren Wu.(2002). Lyapunov-theory-based Radial Basis Function Networks for Adaptive Filtering[J].IEEE Transactions on Circuits and Systems. 49(8):1215-1220.
[77]Kantz,H. (1994). A Robust Method to Estimate the Maximal Lyapunov Exponent of a Time Series[J]. Physics letters. A 185:11,77-87.
[78]Kantz, H.and T.Schreiber(1997). Nonlinear Time Series Analysis[M]. Cambridge:Cambridge Univ.Press.
[79]Karras, G. (1996).Are the Output Effects of Monetary Policy Asymmetric? Evidence from a Sample of European Countries[J].Qxford Bulletin of Economics and Statistics,58:267-278.
[80]Karras, G. and H.Stokes(1999).Are the Output Effects of Money-supply Shock Asymmetric? Evidence from Prices, Consumption and Investment[J], Journal of Macroeconomics 21:713-728.
[81]Keenman, D.M. (1985). A Turkey Non-additivity-type Test for Time Series Nonlinearity [J]. Biometrika,72:39-44.
[82]Kember, G.,and A.C. Fowler (1993). A correlation function for choosing time delays in phase portrait reconstructions [J]. Physical Letters A 179(2):72-80.
[83]Keynes, J.M.(1936). The General Theory of Employment, Interest and Money[M]. London: Macmillan Cambridge University Press.
[84]Kim, H.S., R. J. Eykholt and D. Salas (1999). Nonlinear dynamics, delay times, and embedding windows [J].Physica D 127 (1):48-60.
[85]Kodres L.E.,Papell D.H.(1991). Nonlinear dynamics in foreign exchange futures market[R]. Working paper, Universtiy of Michigan.
[86]Kuan, C.M. and H. White(1990). Predicting Appliance Ownership Using Logit, Nueral Networks and Regression Tree Models[R]. BEBR Working Paper 90-1647.
[87]Kuan, C.M. and T. Liu(1995). Forcasting Exchange Rate Using Feedforward and Recurrent Nueral Networks[J]. Journal of Applied Econometrics 10:347-364.
[88]Kugiumtzis, D.(1996). State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length [J]. Physica D 95(1):13-28.
[89]Kwiathowski, D. and P.C.B. Phillips, P. Schmidt and Y. Shin(1992). Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root:How sure are We that Economic
[90]Time Series have a Unit Root? [J]. Journal of Econometrics 54:159-178.
[91]Kyung-Joong Kim,Sung-Bae Cho(2008).Evolutionary ensemble of diverse artificial neural networks using speciation[J]. Neurocomputing.71:1604-1618.
[92]Lee, D. and P. Schmidt(1996). On the Power of the KPSS Test of Stationarity Against Fractionally-integrated Alternatives[J]. Journal of Econometrics 73:285-302.
[93]Lee,T,-H., H.White and C.W.J Granger(1993). Testing for Neglected Nonlinearity in Time Series Models:A Comparison of Neural Network Methods and Alternative Tests [J]. Journal of Econometrics 56:269-290.
[94]Lei Xu(1993). Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, And Curve Detection[J]. IEEE Transaction on Neural Networks,4(4):636-649.
[95]Lindgren,G. and H. Rootzen(1987). Extremal Values:Theory and Technical Applications[J]. Scandinavian Journal of Statistics 14:241-279.
[96]Liu,T., C.W.J Granger and W. Heller (1992). Using the Correlation Exponent to Decide if an Economic Series is Chaotic[J]. Journal of Applied Econometrics 7S:525-540.
[97]Lo, A.W. (1991). Long-Term Memory in Stock Market Prices [J]. Econometrica 59:1279-1313.
[98]Mandelbrot, B.B.,and M.Taqqu (1979). Robust R/S Analysis of Long Run Serial Correlation. Bulletin of International Statistical Institute 48, Book 3:59-104.
[99]Mankiw,G.N.(1991)The reincarnation ofKeynesian economics[J],NBER Working Paper No.3885.
[100]Mantalos, P.(2000). A Graphical Investigation of the Size and Power of the Grange-Causality Tests inlntegrated-Cointegrated VAR Systems[J], Studies in Non-linear Dynamics and Econometrics 4:17-33.
[101]Martin T.Hagan, Howard B.Demuth and Mark H.Beale著.戴葵等译.神经网络设计[M].北 京：机械工业出版社,2002.
[102]Mitchell,W.C.(1927). Business Cycles:The Problem and its Setting[M]. New York,:National Bureau of Economic Research.
[103]Mcleod, A.I. and W.K. Li (1983). Diagnostic Checking ARMA Time Series Models Using Squared Residual Autocorrelations [J]. Journal of Time Series Analysis 4:169-176.
[104]Moody, J. and C.Darken(1988). Learning with Localized Receptive Fields[C]. In Sejnowski T, Touretzky D, Hinton G, editors, Connectionist Models Summer School, Carnegie Mellon University.
[105]Moody, J.(1994).Prediction risk and architecture selection for neural networks[C].Statistics to Neural Networks:Theory and Pattern Recognition Applications, NATO ASI Series F. New York:178-197.
[106]Mundell,R.A. (1963)Capital mobility and stabilization policy under fixed and flexible exchange rates[J], Canadian Journal of Economics and Political Science,29,475-85
[107]Neftci,S.N.(1984). Are Economic Time Series Asymmetric over the Business Cycles?[J]. Journal of Political Economy,92:301-328.
[108]Packard, N.H., J. P. Crutchfield and J.D. Farmer, et al. (1980). Geometry from a Time Series [J]. Physical Review Letter 45(3):712-716.
[109]Parzen, E. (1962). On Estimation of a Probability Density Function and Mode [J], Annual Math Statistics 33:1065-1076.
[110]Peters, E.E(1991).Chaos and Order in the Capital Markets-a new View of Cycles, Prices and Market Volatility[M]. New York:John Wiley&Sons, Inc.
[111]Peters E.E.(1994). Fractal Market Analysis:Applying Chaos Theory to Investment and Economics[M]. New York:John Wiley & son Inc.
[112]Peters E.E.(1996).Chaos and Order in the Capital Market. Second Ed[M],John Wiley& Sons press.
[113]Philippatos, G.C., Pilarinu,E. and Malliaris, A.G.(1994). Chaotic Behavior in Prices of European Equity Markets:A Comparative Analysis of Major Economic Regions[J]. Journal of Multinational Finance Managemen,3:5-24.
[114]Ramsey, J.B(1969).Tests for Specification Errors in Classical Linear Least Squares Regression Analysis[J]. Journal of the Royal Statistical Society B 31:350-371.
[115]Ramsey, J. and H. Yuan (1989). Bias and Error Bias in Dimension Calculation and their Evaluation in some Simple Models [J]. Physical Letters A 134:287-297.
[116]Richards,G.R.(2000).The Fractal Structure of Exchange Rates:Measurement and Forecasting[J] Journal of International Financial Markets, Institutions and Money.10:163-180.
[117]Rosenstein M.T., J.J. Collins and L.C.De (1993), A Practical Method for Calculating Largest lyapunov Exponents from Small Data Sets [J]. Physica D 65:117-134.
[118]Rosenstein, M.T., J.J.Collins and C.J.De Luca (1994). Reconstruction expansion as a geometry-based framework for choosing proper delay times [J]. Physica D 73(1):82-98.
[119]Ruppert D, M.P.Wand.(1994). Multivariate locally weighted least squares regression[J]. Annals of Statistics 22:1346-1370.
[120]Sato, S., M. Sano, and Y. Sawada (1987). Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in high Dimensional Chaotic Systems [J]. Progress of Theoretical Physics 77:1-5.
[121]Scheinkman, J. and B. Lebanon (1989). Nonlinear Dynamics and Stock Returns [J]. Journal of Business 62:311-337.
[122]Schmidt, P. and P.C.B.Phillips (1992). LM test for a unit root in the presence of deterministic trends[J]. Oxford Bulletin of Economics and Statistics 54,257-287.
[123]Sercu, P., Uppal, R. and C.Van Hulle(1995). The Exchange Rate in the Presence of Transaction Costs:Implications for Tests of Purchasing Power Parity[J]. Journal of Finance 50:1309-1319.
[124]Smith, R.L. (1992). Estimating Dimension in Noisy Chaotic Time Series [J]. Journal of Royal Statistical Society B 54:329-352.
[125]Sowell,F.B.(1990).The fractional unit root distribution[J]. Economica 58:495-505. Srinivas,M. and L.M.Patnaik (1996). Genetic Search:Analysis Using Fitness Moments[J]. IEEE Transactions on Knowledge and Data Engineering 8(1):120-133.
[126]Stutzer, M,J.(1980). Chaotic Dynamics and Bifurcations in a Macro Model[J]. Journal of Economic Dynamics and Control 4(3):353-376.
[127]Taqqu,M.S.,V.Teverosky and W.Willinger(1995). Estimations for long-range dependence:an empirical study[J]. Fractals 3(4):765-788.
[128]Takens, F. (1981). Detecting Strange Attractor in Turbulence. in Dynamical systems and turbulence, Warwich,1980, Lecture Notes in Mathe-matics, Rand and Young eds 898: 366-381.
[129]Tj(?)stheim,D.(1994). Non-linear Time Series:a selective Review[J]. Scandinavian Journal ofStatistics 21:97-130.
[130]Tong,H.(1990). Non-linear Time Series:A Dynamical Systems Approach[M]. Oxford University Press, Oxford.
[131]Tong,H. (1995). A personal overview of non-linear time series analysis from a chaos perspective(with discussion)[J]. Scandinavian Journal of Statistics 22:399-445.
[132]Tsay, R.S.(1986). Nonlinearity Test for Time Series [J]. Biometrika 73:461-466.
[133]Tsay,R..S(2002). Analysis of Finacial Times Series[M]. John Wiley&Sons,Inc,New York.
[134]Vance L. Martin and Kim Sawyer (1994), Statistic techniques for modeling nonlinearities. In John Creedy, Vance L. Martin(ed.), Chaos and nonlinear models in economics:theory and applications. Edward Elgar Publishing Company:113-134.
[135]White, H.(1988). Economic Prediction Using Nueral Networks:The Case of IBM Stock Prices[C]. Proceedings of the IEEE Second International Conference on Neural Networks 2:451-458.
[136]White, H.(1989). Some Asymptotic Results for Learning in Single Hidden-layer Feedforward Network Models[J]. Journal of the American Statistical Association 84:1003-1013.
[137]Wolf A., J.B. Swift, H.L. Swinney and J.A. Vastano (1985). Determining Lyapunov exponents from a time series [J]. Physica D 16:285-317.
[138]Xiao-Ming Li.(2006). A Revisit Of International Stock Market Linkages:New Evidence From Rank Tests For Nonlinear Cointegration[J]. Scottish Journal of Political Economy 2:174-197.
[139]Yao,Q. and Tong,H.(1995a). On Initial-condition Sensitivity and Prediction in Nonlinear Stochastic Systems[J]. Bull. Int. Statist. Inst.50:395-412.
[140]Yao,Q. and Tong,H.(1995b). On Prediction and Chaos in Stochastic Systems[J]. Philosophical transactions A:mathematical, physical and engineering sciences,348 (1688):357-369.
[141]Yule, G.U.(1927). On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunsport Numbers[J]. Philosophical Transactions 226A:267-298.
[142]Zhang Qinghua, Benveniste, A. (1992). Wavelet Networks[J]. IEEE Transactions on Neural Networks 3(6):888-898.
[143]陈守东,韩广哲,荆伟.主要股票市场指数与我国股票市场指数间的协整分析[J].数量经济技术经济研究,2003(5)：124-129.
[144]陈小平,赵鹤鸣,杨新艳.遗传前馈神经网络在函数逼近中的应用[J].计算机工程.2008,34(20)24-28.
[145]储海林,吕小宁,李哲.分形与统计学[J].统计研究,2004(2)：35-37.
[146]郑湄,苗佳.应用协整检验对中国股市及美、英股市联动关系的分析[J].山东社会科学,2004(12)：113-115.
[147]范剑青,姚琦伟著.陈敏译.非线性时间序列-建模,预报及应用[M].高等教育出版社,2005.
[148]韩非,肖辉.中美股市间的联动性分析[J],金融研究,2005(11)：117-129
[149]黄忠明,吴志红,刘全喜.几种用于非线性函数逼近的神经网络方法研究[J].兵工自动化.2009,28(10)：88-92.
[150]黄建国,罗航,王厚军,龙兵.运用GA-BP神经网络研究时间序列的预测[J].电子科技大学学报.2009,38(5)：687-692.
[151]冯今朝,王仲生.基于LM优化算法的神经网络在航空发动机转子故障诊断中的应用[J].宇航计测技术.2007,27(2)：18-21,49.
[152]梁勇,孟桥,陆佶人.Lyapunov指数的算法改进与加权预测[J].声学技术,2006,(05)：463-467.
[153]雷钦礼.非线性协整模型：理论与方法[J].统计研究,2009(3)：81-91.
[154]林文夫著,冉启康,朱保华译.计量经济学.上海财经济大学.2005.10.
[155]林嘉宇,王跃科,黄芝平,等.语音信号相空间重构中时间延迟的选择—复自相关法[J].信号处理,1999,15(3)：220-225.
[156]罗伯特S.平狄克&丹尼尔L.鲁宾费尔德著.钱小平等译.计量经济模型与经济预测(第4版)机械工业出版社1999.11.
[157]刘汉中,傅元海.基于残差的非对称单位根自助法检验研究[J].数量经济技术经济研究,2008(8)：151-160.
[158]李春鑫,李天伟,王孝通.基于小波模糊网络的非线性函数逼近方法的研究[J].计算机测量与控制.2006,14(3)：322-323,338.
[159]李明国,郁文贤.神经网络的函数逼近理论[J].国防科技大学学报,1998,20(4)：70-76.
[160]李洋.小波过程神经网络相关理论及其应用研究[D].博士论文.哈尔滨工业大学,2008.
[161]李美洲.门限及分数维分析及其在经济中的应用[D].博士论文.暨南大学,2008.
[162]李选举.Box-Cox变换及其在MathCAD上的实现[J].数量经济技术经济研究,2000,4：42-44.
[163]乔俊飞,张颖.一种多层前馈神经网络的快速修剪算法[J].智能系统学报.2008,3(2)：173-176.
[164]活尔特.恩德斯(Walter Enders)著.杜江谢志超译.应用计量经济学：时间序列分析(第二版)[M].高等教育出版社.2006.6.
[165]L.沃塞曼[美]著,吴喜之译.现代非参数统计[M].科学出版社.北京：2008.
[166]王国松,杨扬.国际资本流动下我国货币需求函数稳定性检验[J].财经研究,2006(10)：17-25.
[167]王少平.单位根和协整及其结构突变的理论与应用研究(清华大学博士论文)2002.
[168]王忠玉.混沌的计量经济学简评[J].统计研究,2000(2)：61.
[169]王春玲.基于径向基函数网络的非线性系统自适应逆控制[D].硕士论文,山东大学,2007.
[170]施锡铨,艾克凤.股票市场风险的多重分形分形[J].统计研究,2004(9)：33-36.
[171]石建民.股票市场、货币需求与总量经济：一般均衡分析[J].经济研究,2001(5)：45-52.
[172]舒晓惠,雷钦礼,宋金奇.单位根的秩检验及其应用研究[J].统计研究,2009(9)：101-107.
[173]舒晓惠,雷钦礼,陈一非.中国与国际股市的协整分析——基于一种新的非线性协整秩检验方法[J].山西财经大学学报,2010(1)：17-29.
[174]孙青华,张世英.长记忆向量时间序列的非线性协整关系研究[J].天津大学学报,200235(3)：327-331.
[175]田旭光,宋彤,刘宇新.结合遗传算法优化BP神经网络的结构和参数[J].计算机应用与软件,2004,21(6)：69-71.
[176]谢益辉,朱钰.Bootstrap方法的历史发展和前沿研究[J].统计与信息论坛,2008(2)：90-96.
[177]杨庆,秦伟良.R／S和修正R／S方法的实证分析[J].统计与决策,2003(11)：18-19.
[178]杨建刚.人工神经网络实用教程[M].杭州：浙江大学出版社,2001.
[179]杨国为,王守觉,闫庆旭.分式线性神经网络及其非线性逼近能力研究[J].计算机学报.2007,30(2)：189-199.
[180]叶阿忠.非参数经济学[M].南开大学出版,天津：2003.7.
[181]叶阿忠.非线性协整的非参数检验方法[J].预测,2001(1)：79-80.
[182]易行健.关于中国股票市场对货币需求总量与结构影响的分析[J],经济科学,2004
[183]易行健.经济开放条件下的货币需求函数：中国的经验[J],世界经济,2006(4)：49-59.
[184]俞世典,陈守东,黄立华.主要股票指数的联动分析[J].统计研究,2001(8)：42-46.
[185]张世英樊智.协整理论与波动模型.清华大学出版社.2004.
[186]张贤达(1996).时间序列分析—高阶统计量方法[M].北京：清华大学出版社：31-45.
[187]张丹,于朝民,付永杰.基于人工神经网络的传感器非线性拟合方法的研究[J].工业计量.2004,14(5)：31-33.
[188]张喜彬,张世英.关于单整时间序列非线性变换的研究[J].系统工程学报.1998,13(2)：70-77.
[189]张昭昭,沈学利,乔俊飞.基于权值e指数信息熵的前馈网络修剪算法[J].辽宁工程技术大学学报(自然科学版).2009,28(3)：439-441.
[190]钟登华.非线性随机最佳变换模型及其应用[J].系统工程学报.1996,11(3)：84-89.
[191]赵贵兵,石炎福,段文锋,余华瑞.从混沌时间序列同时计算关联维和Kolmogorov熵[J].计算物理,1999,15(3)：309-315.
[192]张尧庭.关于度量变量之间的相关程度[J].上海财经大学学报,1999(12)：60-63.
[193]周建(2005).时间序列建模中滞后阶数选取准则函数的检测效力及其特征[J].系统工程理论与实践,2005年第11期：20-27.
[194]中国人民银行研究局课题组,中国股票市场发展与货币政策完善[J],金融研究,2002(4)：1-12.