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Volumn 120, Issue 1, 2004, Pages 1-33

Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos

Author keywords

Artificial neural networks; Nonlinear dynamics; Nonlinear time series; Nonparametric regression; Sieve estimation

Indexed keywords

ASYMPTOTIC STABILITY; CHAOS THEORY; INTEGRATION; LINEAR EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; REGRESSION ANALYSIS; THEOREM PROVING;

EID: 1542400411     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(03)00205-7     Document Type: Article
Times cited : (101)

References (39)
  • 1
    • 0002503853 scopus 로고    scopus 로고
    • Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100
    • Abhyankar A., Copeland L.S., Wong W. Uncovering nonlinear structure in real-time stock-market indexes. the S&P 500, the DAX, the Nikkei 225, and the FTSE-100 Journal of Business and Economic Statistics. 15:1997;1-14.
    • (1997) Journal of Business and Economic Statistics , vol.15 , pp. 1-14
    • Abhyankar, A.1    Copeland, L.S.2    Wong, W.3
  • 2
    • 0001758906 scopus 로고
    • Heteroskedasticity and autocorrelation consistent covariance matrix estimation
    • Andrews D.W.K. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica. 59:1991;817-858.
    • (1991) Econometrica , vol.59 , pp. 817-858
    • Andrews, D.W.K.1
  • 3
    • 0003045633 scopus 로고    scopus 로고
    • Local Lyapunov exponents: Predictability depends on where you are
    • W.A. Barnett, A.P. Kirman, & M. Salmon. Cambridge: Cambridge University Press
    • Bailey B.A. Local Lyapunov exponents: predictability depends on where you are. Barnett W.A., Kirman A.P., Salmon M. Nonlinear Dynamics and Economics. 1996;345-359 Cambridge University Press, Cambridge.
    • (1996) Nonlinear Dynamics and Economics , pp. 345-359
    • Bailey, B.A.1
  • 6
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory. 39:1993;930-945.
    • (1993) IEEE Transactions on Information Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 9
    • 0000921080 scopus 로고    scopus 로고
    • Heterogeneous beliefs and routes to chaos in a simple asset pricing model
    • Brock W.A., Hommes C.H. Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control. 22:1998;1235-1274.
    • (1998) Journal of Economic Dynamics and Control , vol.22 , pp. 1235-1274
    • Brock, W.A.1    Hommes, C.H.2
  • 10
    • 0035392123 scopus 로고    scopus 로고
    • Semiparametric ARX neural-network models with an application to forecasting inflation
    • Chen X., Racine J., Swanson N.R. Semiparametric ARX neural-network models with an application to forecasting inflation. IEEE Transactions on Neural Networks. 12:2001;674-683.
    • (2001) IEEE Transactions on Neural Networks , vol.12 , pp. 674-683
    • Chen, X.1    Racine, J.2    Swanson, N.R.3
  • 11
    • 0004403816 scopus 로고    scopus 로고
    • Sieve extremum estimates for weakly dependent data
    • Chen X., Shen X. Sieve extremum estimates for weakly dependent data. Econometrica. 66:1998;289-314.
    • (1998) Econometrica , vol.66 , pp. 289-314
    • Chen, X.1    Shen, X.2
  • 12
    • 0033096783 scopus 로고    scopus 로고
    • Improved rates and asymptotic normality for nonparametric neural network estimators
    • Chen X., White H. Improved rates and asymptotic normality for nonparametric neural network estimators. IEEE Transactions on Information Theory. 45:1999;682-691.
    • (1999) IEEE Transactions on Information Theory , vol.45 , pp. 682-691
    • Chen, X.1    White, H.2
  • 13
    • 84986409797 scopus 로고
    • Lyapunov exponents as a nonparametric diagnostic for stability analysis
    • Dechert W.D., Gençay R. Lyapunov exponents as a nonparametric diagnostic for stability analysis. Journal of Applied Econometrics. 7:1992;S41-S60.
    • (1992) Journal of Applied Econometrics , vol.7 , pp. 41-S60
    • Dechert, W.D.1    Gençay, R.2
  • 14
  • 16
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann J.-P., Ruelle D. Ergodic theory of chaos and strange attractors. Reviews of Modern Physics. 57:1985;617-656.
    • (1985) Reviews of Modern Physics , vol.57 , pp. 617-656
    • Eckmann, J.-P.1    Ruelle, D.2
  • 17
    • 0001414087 scopus 로고
    • Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data
    • Ellner S., Gallant A.R., McCaffrey D., Nychka D. Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data. Physics Letter A. 153:1991;357-363.
    • (1991) Physics Letter A , vol.153 , pp. 357-363
    • Ellner, S.1    Gallant, A.R.2    Mccaffrey, D.3    Nychka, D.4
  • 19
    • 0010193928 scopus 로고
    • Inequalities for the norms of a function and its derivatives in metric Lp
    • Gabushin V.N. Inequalities for the norms of a function and its derivatives in metric Lp. Matematicheskie Zametki. 1:1967;291-298.
    • (1967) Matematicheskie Zametki , vol.1 , pp. 291-298
    • Gabushin, V.N.1
  • 20
    • 0026449851 scopus 로고
    • On learning the derivatives of an unknown mapping with multilayer feedforward networks
    • Gallant A.R., White H. On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks. 5:1992;129-138.
    • (1992) Neural Networks , vol.5 , pp. 129-138
    • Gallant, A.R.1    White, H.2
  • 21
    • 0001062715 scopus 로고    scopus 로고
    • A statistical framework for testing chaotic dynamics via Lyapunov exponents
    • Gençay R. A statistical framework for testing chaotic dynamics via Lyapunov exponents. Physica D. 89:1996;261-266.
    • (1996) Physica D , vol.89 , pp. 261-266
    • Gençay, R.1
  • 22
    • 0000547548 scopus 로고
    • An algorithm for the n Lyapunov exponents of an n -dimensional unknown dynamical system
    • Gençay R., Dechert W.D. An algorithm for the. n Lyapunov exponents of an n -dimensional unknown dynamical system Physica D. 59:1992;142-157.
    • (1992) Physica D , vol.59 , pp. 142-157
    • Gençay, R.1    Dechert, W.D.2
  • 24
    • 0035400224 scopus 로고    scopus 로고
    • New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation
    • Giannerini S., Rosa R. New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation. Physica D. 155:2001;101-111.
    • (2001) Physica D , vol.155 , pp. 101-111
    • Giannerini, S.1    Rosa, R.2
  • 25
    • 0000052574 scopus 로고
    • An invariance principle for weakly dependent sequences of random variables
    • Herrndorf N. An invariance principle for weakly dependent sequences of random variables. Annals of Probability. 12:1984;141-153.
    • (1984) Annals of Probability , vol.12 , pp. 141-153
    • Herrndorf, N.1
  • 26
    • 0001307541 scopus 로고
    • Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives
    • Hornik K., Stinchcombe M., White H., Auer P. Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives. Neural Computation. 6:1994;1262-1275.
    • (1994) Neural Computation , vol.6 , pp. 1262-1275
    • Hornik, K.1    Stinchcombe, M.2    White, H.3    Auer, P.4
  • 27
    • 84948516717 scopus 로고
    • Artificial neural networks: An econometric perspective
    • Kuan C.-M., White H. Artificial neural networks. an econometric perspective Econometric Reviews. 13:1994;1-91.
    • (1994) Econometric Reviews , vol.13 , pp. 1-91
    • Kuan, C.-M.1    White, H.2
  • 29
    • 0030119952 scopus 로고    scopus 로고
    • Random approximants and neural networks
    • Makovoz Y. Random approximants and neural networks. Journal of Approximation Theory. 85:1996;98-109.
    • (1996) Journal of Approximation Theory , vol.85 , pp. 98-109
    • Makovoz, Y.1
  • 34
    • 21844526328 scopus 로고
    • Random walks, breaking trend functions, and the chaotic structure of the velocity of money
    • Serletis A. Random walks, breaking trend functions, and the chaotic structure of the velocity of money. Journal of Business and Economic Statistics. 13:1995;453-458.
    • (1995) Journal of Business and Economic Statistics , vol.13 , pp. 453-458
    • Serletis, A.1
  • 35
    • 0031321079 scopus 로고    scopus 로고
    • On methods of sieves and penalization
    • Shen X. On methods of sieves and penalization. Annals of Statistics. 25:1997;2555-2591.
    • (1997) Annals of Statistics , vol.25 , pp. 2555-2591
    • Shen, X.1
  • 36
    • 21844489169 scopus 로고
    • Convergence rate of sieve estimates
    • Shen X., Wong W.H. Convergence rate of sieve estimates. Annals of Statistics. 22:1994;580-615.
    • (1994) Annals of Statistics , vol.22 , pp. 580-615
    • Shen, X.1    Wong, W.H.2
  • 37
    • 0037298065 scopus 로고    scopus 로고
    • Is there chaos in the world economy? A nonparametric test using consistent standard errors
    • Shintani M., Linton O. Is there chaos in the world economy? A nonparametric test using consistent standard errors. International Economic Review. 44:2003;331-358.
    • (2003) International Economic Review , vol.44 , pp. 331-358
    • Shintani, M.1    Linton, O.2
  • 39
    • 0002835545 scopus 로고    scopus 로고
    • The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series
    • Whang Y.-J., Linton O. The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series. Journal of Econometrics. 91:1999;1-42.
    • (1999) Journal of Econometrics , vol.91 , pp. 1-42
    • Whang, Y.-J.1    Linton, O.2


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