Martingales, nonlinearity, and chaos

Journal of Economic Dynamics and Control - Tập 24 Số 5-7 - Trang 703-724 - 2000
William A. Barnett1, Apostolos Serletis2
1Department of Economics, Campus Box 1208, Washington University, One Brookings Drive, St. Louis, MO 63130-4810, USA
2Department of Economics, The University of Calgary, Calgary, Alberta T2N 1N4, USA

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Abhyankar, 1995, Nonlinear dynamics in real-time equity market indices: evidence from the UK, Economic Journal, 105, 864, 10.2307/2235155

Abhyankar, 1997, 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, 1, 10.2307/1392068

Baillie, 1996, Long memory processes and fractional integration in econometrics, Journal of Econometrics, 73, 5, 10.1016/0304-4076(95)01732-1

Barnett, W.A., Chen, P., 1988. The aggregation-theoretic monetary aggregates are chaotic and have strange attractors: an econometric application of mathematical chaos. In: Barnett, W.A., Berndt, E.R., White, H. (Eds.), Dynamic Econometric Modeling. Cambridge University Press, Cambridge, UK.

Barnett, 1995, Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size, Journal of Economic Behavior and Organization, 27, 301, 10.1016/0167-2681(94)00082-P

Barnett, W.A., Gallant, A.R., Hinich, M.J., Jungeilges, J., Kaplan, D., Jensen, M.J., 1996. An experimental design to compare tests of nonlinearity and chaos. In: Barnett, W.A., Kirman, A., Salmon, M. (Eds.), Nonlinear Dynamics in Economics. Cambridge University Press, Cambridge, UK.

Barnett, 1997, A single-blind controlled competition among tests for nonlinearity and chaos, Journal of Econometrics, 82, 157, 10.1016/S0304-4076(97)00081-X

Barnett, 1992, Empirical chaotic dynamics in economics, Annals of Operations Research, 37, 1, 10.1007/BF02071045

Benhabib, J., 1992. Cycles and Chaos in Economic Equilibrium. Princeton University Press, Princeton, NJ.

Bickel, P.J., Bühlmann, P., 1996. What is a linear process? Proceedings of the National Academy of Science, USA, Statistics Section 93, pp. 12, 128–12,131.

Brillinger, 1965, An introduction to the polyspectrum, Annals of Mathematical Statistics, 36, 1351, 10.1214/aoms/1177699896

Brock, 1996, A test for independence based on the correlation dimension, Econometric Reviews, 15, 197, 10.1080/07474939608800353

Brock, W.A., Hsieh, D.A., LeBaron, B., 1991. Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence. MIT Press, Cambridge, MA.

Brock, W.A., Sayers, C., 1988. Is the business cycle characterized by deterministic chaos? Journal of Monetary Economics 22, 71–90.

Brockett, 1988, Bispectral-based tests for the detection of gaussianity and nonlinearity in time series, Journal of the American Statistical Association, 83, 657, 10.2307/2289288

Campbell, J.Y., Lo, A.W., MacKinlay, A.C., 1997. The Econometrics of Financial Markets. Princeton University Press, Princeton, NJ.

Cochrane, J.H., 1988. How big is the random walk in GNP? Journal of Political Economy 96, 893–920.

DeCoster, 1991, Nonlinear monetary dynamics, Journal of Business and Economic Statistics, 9, 455, 10.2307/1391245

DeCoster, 1994, Reply, Journal of Business and Economic Statistics, 12, 136, 10.2307/1391931

Dickey, 1981, Likelihood ratio tests for autoregressive time series with a unit root, Econometrica, 49, 1057, 10.2307/1912517

Fama, 1965, The behavior of stock market prices, Journal of Business, 38, 34, 10.1086/294743

Fama, 1970, Efficient capital markets: a review of theory and empirical work, Journal of Finance, 25, 383, 10.2307/2325486

Fama, 1988, Permanent and temporary components of stock prices, Journal of Political Economy, 96, 246, 10.1086/261535

Frank, 1988, International chaos, European Economic Review, 32, 569, 10.1016/0014-2921(88)90018-9

Frank, 1988, Some evidence concerning macroeconomic chaos, Journal of Monetary Economics, 22, 423, 10.1016/0304-3932(88)90006-2

Frank, 1989, Measuring the strangeness of gold and silver rates of return, Review of Economic Studies, 56, 553, 10.2307/2297500

Gallant, 1992, On learning the derivatives of an unknown mapping with multilayer feedforward networks, Neural Networks, 5, 129, 10.1016/S0893-6080(05)80011-5

Gencay, 1992, An algorithm for the n-Lyapunov exponents of an n-dimensional unknown dynamical system, Physica D, 59, 142, 10.1016/0167-2789(92)90210-E

Ghashghaie, 1996, Turbulent cascades in foreign exchange markets, Nature, 381, 767, 10.1038/381767a0

Grandmont, 1985, On endogenous competitive business cycles, Econometrica, 53, 995, 10.2307/1911010

Granger, 1994, Is chaotic economic theory relevant for economics? A review article of: Jess Benhabib: cycles and chaos in economic equilibrium, Journal of International and Comparative Economics, 3, 139

Granger, 1995, Modelling nonlinear relationships between extended-memory variables, Econometrica, 63, 265, 10.2307/2951626

Grassberger, 1983, Characterization of strange attractors, Physical Review Letters, 50, 346, 10.1103/PhysRevLett.50.346

Hinich, 1982, Testing for gaussianity and linearity of a stationary time series, Journal of Time Series Analysis, 3, 169, 10.1111/j.1467-9892.1982.tb00339.x

Hinich, M.J., Patterson, D., 1989. Evidence of nonlinearity in the trade-by-trade stock market return generating process. In: Barnett, W.A., Geweke, J., Shell, K. (Eds.), Economic Complexity: Chaos, Bubbles, and Nonlinearity. Cambridge University Press, Cambridge, UK.

Hsieh, 1991, Chaos and nonlinear dynamics: applications to financial markets, Journal of Finance, 46, 1839, 10.2307/2328575

Kaplan, 1994, Exceptional events as evidence for determinism, Physica D, 73, 38, 10.1016/0167-2789(94)90224-0

Koedijk, 1992, Tail estimates of east european exchange rates, Journal of Business and Economic Statistics, 10, 83, 10.2307/1391807

Lee, 1993, Testing for neglected nonlinearities in time series models, Journal of Econometrics, 56, 269, 10.1016/0304-4076(93)90122-L

LeRoy, 1989, Efficient capital markets and martingales, Journal of Economic Literature, 27, 1583

Lo, 1988, Stock market prices do not follow random walks: evidence from a simple specification test, Review of Financial Studies, 1, 41, 10.1093/rfs/1.1.41

Mandelbrot, 1963, The variation of certain speculative stock prices, Journal of Business, 36, 394, 10.1086/294632

McCaffrey, 1992, Estimating the Lyapunov exponent of a chaotic system with nonparametric regression, Journal of the American Statistical Association, 87, 682, 10.2307/2290206

Nelson, 1982, Trends and random walks in macroeconomic time series, Journal of Monetary Economics, 10, 139, 10.1016/0304-3932(82)90012-5

Nychka, 1992, Finding chaos in noisy systems, Journal of the Royal Statistical Society B, 54, 399

Perron, 1989, The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 1361, 10.2307/1913712

Poterba, 1988, Mean reversion in stock prices: evidence and implications, Journal of Financial Economics, 22, 27, 10.1016/0304-405X(88)90021-9

Radunskaya, 1994, Comparing random and deterministic series, Economic Theory, 4, 765, 10.1007/BF01212029

Ramsey, 1994, Comment on ‘Nonlinear monetary dynamics’ by DeCoster and Mitchell, Journal of Business and Economic Statistics, 12, 135, 10.2307/1391930

Ramsey, 1990, The statistical properties of dimension calculations using small data sets: some economic applications, International Economic Review, 31, 991, 10.2307/2527026

Ruelle, 1990, Deterministic chaos: the science and the fiction, Proceedings of the Royal Society of London A, 427(1873), 241, 10.1098/rspa.1990.0010

Scheinkman, 1989, Nonlinear dynamics and stock returns, Journal of Business, 62, 311, 10.1086/296465

Schwartz, 1978, Estimating the dimension of a model, The Annals of Statistics, 6, 461, 10.1214/aos/1176344136

Serletis, 1995, Random walks, breaking trend functions, and the chaotic structure of the velocity of money, Journal of Business and Economic Statistics, 13, 453, 10.2307/1392390

Serletis, 1997, Chaos in East European black-market exchange rates, Research in Economics, 51, 359, 10.1006/reec.1997.0050

Summers, 1986, Does the stock market rationally reflect fundamental values, Journal of Finance, 41, 591, 10.2307/2328487

Takens, F., 1981. Detecting strange attractors in turbulence. In: Rand, D., Young, L. (Eds.), Dynamical Systems and Turbulence. Springer, Berlin.

Takens, F., 1997. The effect of small noise on systems with chaotic dynamics. In: van Strien, S.J., Verduyn Lunel, S.M. (Eds.), Stochastic and Spatial Structures of Dynamical Systems. North-Holland, Amsterdam.

White, 1989, Some asymptotic results for learning in single hidden-layer feedforward network models, Journal of the American Statistical Association, 84, 1003, 10.2307/2290076

Wolf, 1985, Determining Lyapunov exponents from a time series, Physica 16 D, 16, 285, 10.1016/0167-2789(85)90011-9