Testing for nonlinearity in time series: the method of surrogate data

Nicolis, 1984, Nature, 311, 529, 10.1038/311529a0 Grassberger, 1986, Nature, 323, 609, 10.1038/323609a0 Nicolis, 1987, Nature, 326, 523, 10.1038/326523b0 Grassberger, 1987, Nature, 326, 524, 10.1038/326524a0 Osborne, 1986, Physica D, 23, 75, 10.1016/0167-2789(86)90113-2 Mayer-Kress, 1988, Vol. I, 122 Osborne, 1989, Physica D, 35, 357, 10.1016/0167-2789(89)90075-4 Provenzale, 1991, Physica D, 47, 361, 10.1016/0167-2789(91)90036-9 Theiler, 1991, Phys. Lett. A, 155, 480, 10.1016/0375-9601(91)90651-N Ramsey, 1989, Phys. Lett. A, 134, 287, 10.1016/0375-9601(89)90638-5 Theiler, 1990, Phys. Rev. A, 41, 3038, 10.1103/PhysRevA.41.3038 Takens, 1984 1985, Vol. 1125, 99 Caswell, 1986, Dimensions and Entropies in Chaotic Systems - Quantification of Complex Behavior, Vol. 32, 123 Holzfuss, 1986, Dimensions and Entropies in Chaotic Systems - Quantification of Complex Behavior, Vol. 32, 114 Theiler, 1988, Quantifying Chaos: Practical Estimation of the Correlation Dimension Möller, 1989, Phys. Lett. A, 138, 176, 10.1016/0375-9601(89)90023-6 Theiler, 1990, J. Opt. Soc. Am. A, 7, 1055, 10.1364/JOSAA.7.001055 Smith, 1992, Nonlinear Modeling and Forecasting, Vol. XII, 115 Theiler, 1992, Nonlinear Modeling and Forecasting, Vol. XII, 163 Subba Rao, 1980, J. Time Series Anal., 1, 145, 10.1111/j.1467-9892.1980.tb00308.x Hinich, 1982, J. Time Series Anal., 3, 169, 10.1111/j.1467-9892.1982.tb00339.x McLeod, 1983, J. Time Series Anal., 4, 269, 10.1111/j.1467-9892.1983.tb00373.x Keenan, 1985, Biometrika, 72, 39, 10.1093/biomet/72.1.39 Tsay, 1986, Biometrika, 73, 461, 10.1093/biomet/73.2.461 Tsay, 1991, Stat. Sin., 1, 431 Tong, 1990 Efron, 1979, SIAM Rev., 21, 460, 10.1137/1021092 Tsay, 1992, Appl. Stat., 41, 1, 10.2307/2347612 Scheinkman, 1989, J. Business, 62, 311, 10.1086/296465 Breeden, 1992, Nonlinear analysis of data sampled nonuniformly in time, Physica D, 58, 273, 10.1016/0167-2789(92)90115-4 Uhlenbeck, 1930, Phys. Rev., 36, 823, 10.1103/PhysRev.36.823 1954 Kaplan, 1990, Circulation Res., 67, 886, 10.1161/01.RES.67.4.886 Brock, 1986 T.-H. Lee, H. White and C.W.J. Granger, Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests J. Econometrics, to appear. Kostelich, 1987, 141 Theiler, 1987, Phys. Rev. A, 36, 4456, 10.1103/PhysRevA.36.4456 Grassberger, 1990, Phys. Lett. A, 148, 63, 10.1016/0375-9601(90)90577-B Grassberger, 1983, Phys. Rev. Lett., 50, 346, 10.1103/PhysRevLett.50.346 Grassberger, 1983, Physica D, 9, 189, 10.1016/0167-2789(83)90298-1 Takens, 1983, Invariants related to dimension and entropy, Atas do 13° Colóqkio Brasiliero de Matemática Ellner, 1988, Phys. Lett. A, 133, 128, 10.1016/0375-9601(88)90772-4 Farmer, 1988, 277 Casdagli, 1992, 131 Casdagli, 1992, Chaos and deterministic versus stochastic nonlinear modeling, J. R. Stat. Soc. B, 54, 303 Sano, 1985, Phys. Rev. Lett., 55, 1082, 10.1103/PhysRevLett.55.1082 Eckmann, 1985, Rev. Mod. Phys., 57, 617, 10.1103/RevModPhys.57.617 Eckmann, 1986, Phys. Rev. A, 34, 4971, 10.1103/PhysRevA.34.4971 Ellner, 1991, Phys. Lett. A, 153, 357, 10.1016/0375-9601(91)90958-B D. McCaffrey, S. Ellner, A.R. Gallant and D. Nychka, Estimating the Lyapunov exponent of a chaotic system with nonparametric regression, J. Am. Stat. Assoc., to appear. Nychka, 1992, J. R. Stat. Soc. B, 54, 399 Schreiber, 1991, Phys. Lett. A, 160, 411, 10.1016/0375-9601(91)90237-3 W.A. Brock, J. Lakonishok and B. LeBaron, Simple technical trading rules and the stochastic properties of stock returns, J. Finance, to appear. Blackman, 1959 Hénon, 1976, Commun. Math. Phys., 50, 69, 10.1007/BF01608556 Mackey, 1977, Science, 197, 287, 10.1126/science.267326 Theiler, 1986, Phys. Rev. A, 34, 2427, 10.1103/PhysRevA.34.2427 Haucke, 1987, Physica D, 25, 307, 10.1016/0167-2789(87)90106-0 Rapp, 1986, 175 Rapp, 1989, Brain Topography, 2, 99, 10.1007/BF01128848 Yule, 1927, Philos. Trans. R. Soc. London A, 226, 267, 10.1098/rsta.1927.0007 Tong, 1980, J. R. Stat. Soc. B, 42, 245 Weiss, 1990, Phil. Trans. R. Soc. London A, 330, 617, 10.1098/rsta.1990.0042 Kurths, 1990, Solar Phys., 126, 407, 10.1007/BF00153060 Weigend, 1990, Intern. J. Neural Systems, 1, 193, 10.1142/S0129065790000102 Mundt, 1991, J. Geophys. Res., 96, 1705, 10.1029/90JA02150 Weigend, 1992, Predicting sunspots and exchange rates with connectionist networks, Vol. XII, 397 L. Smith, Identification and prediction of deterministic dynamical systems, this volume. Ellner, 1991, Detecting low-dimensional chaos in population dynamics data: a critical review, 65 Brock, 1988, J. Monetary Econ., 22, 71, 10.1016/0304-3932(88)90170-5 Brock, 1989, Statistical inference theory for measures of complexity in chaos theory and nonlinear science, 79 Brock, 1992, Nonlinear Modeling and Forecasting, Vol. XII, 137 Hsieh, 1989, J. Business, 62, 339, 10.1086/296466 Hsieh, 1991, J. Finance, 46, 1839, 10.2307/2328575