The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series

Journal of Econometrics

Volumn 91, Issue 1, 1999, Pages 1-42

  Whang, Yoon Jae ^a   Linton, Oliver ^b  

^a Ewha Womans University   (South Korea)

^b YALE UNIVERSITY   (United States)

Author keywords

Chaos; Kernel; Nonlinear dynamics; Nonparametric regression; Semi parametric

Indexed keywords

EID: 0002835545     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(98)00047-5     Document Type: Article

References (38)

1. Andrews, D.W.K., 1989. Stochastic equicontinuity for semiparametric models. Unpublished manuscript, Cowles Foundation, Yale University.
2. Andrews, D.W.K., 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817-858.
3. Andrews, D.W.K., 1994. Asymptotics for semiparametric econometric models via stochastic equicontinuity. Econometrica 62, 43-72.
4. Andrews, D.W.K., 1995. Nonparametric Kernel estimation for semiparametric models. Econometric Theory 11, 560-596.
5. Andrews, D.W.K., Monahan, J.C., 1992. An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953-966.
6. Bierens, H., 1987. Kernel estimators of regression functions. In: Bewley, T.F. (Ed.), Advances in Econometrics: Fifth World Congress, vol 1. Cambridge University Press, Cambridge.
7. Brock, W.A., 1986. Distinguishing random and deterministic systems. Journal of Economic Theory 40, 168-195.
8. Chan, K.S., Tong, H., 1994. A note on noisy chaos. Journal of the Royal Statistical Society Series B 56, 301-311.
9. Cheng, B., Tong, H., 1992. On consistent nonparametric order determination and chaos. Journal of the Royal Statistical Society, Series B 54, 427-449.
10. Dechert, W.D., Gençay, R., 1992. Lyapunov exponents as a nonparametric diagnostic for stability analysis. Journal of Applied Econometrics 7, S41-S60.
11. De Jong, R.M., Davidson, J., 1996. Consistency of kernel estimators of heteroskedastic and autocorrelated covariance matrices. CentER Discussion paper no. 9652, Tilburg University.
12. Doukhan, P., 1994. Mixing: Properties and Examples. Springer, Berlin.
13. Eckmann, J.P., Kamphorst, S.O., Ruelle, D., Ciliberto, S., 1986. Lyapunov exponents from time series. Physics Review A 34, 4971-4979.
14. Folland, G.B., 1984, Real Analysis: Modern Techniques and their Applications. Wiley, New York.
15. Furstenberg, H., Kesten, H., 1960. Products of random matrices. The Annals of Mathematical Statistics 31, 457-469.
16. Gallant, A.R., 1987. Nonlinear Statistical Models. Wiley, New York.
17. Gençay, R., 1996. A statistical framework for testing chaotic dynamics via Lyapunov exponents. Physica D 89, 261-266.
18. Gençay, R., Dechert, W.D., 1992. An algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system. Physica D 59, 142-157.
19. Gnedenko, B.V., 1943. Sur la distribution limite du term maximum d'une série aléatoire. Annals of Mathematical Statistics 44, 423-453.
20. Hansen, B.E., 1992. Consistent covariance matrix estimation for dependent heterogeneous processes. Econometrica 60, 967-972.
21. Härdle, W., Hart, J., Marron, J.S., Tsybakov, A.B., 1992. Bandwidth choice for average derivative estimation. Journal of the American Statistical Association 87, 218-226.
22. Härdle, W., Stoker, T., 1989. Estimating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84, 986-995.
23. Hengartner, N.W., Linton, O.B., 1996. Nonparametric regression estimation at design poles and zeros. Canadian Journal of Statistics 24, 583-591.
24. Herrndorf, N., 1984. An invariance principle for weakly dependent sequences of random variables. Annals of Probability 12, 141-153.
25. Leadbetter, M.R., Rootzén, H., 1988. Extremal theory for stochastic processes. Annals of Probability 16, 431-478.
26. LeBaron B., 1997. Has chaos theory found any useful application in the social sciences. Manuscript, University of Wisconsin, http://www.ssc.wisc.edu/b̃lebaron.
27. Loynes, R.M., 1965. Extreme values in uniformly mixing stationary stochastic processes. Annals of Mathematical Statistics 66, 993-999.
28. McCaffrey, D., Ellner, S., Gallant, A.R., Nychka, D., 1992. Estimating the Lyapunov exponent of a chaotic system with nonparametric regression. Journal of the American Statistical Association 87, 682-695.
29. Masry, E., 1996. Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571-599.
30. Newey, W.K., 1994. The asymptotic variance of semiparametric estimators. Econometrica 62, 1349-1382.
31. Newey, W.K., 1995. Convergence rates for series estimators, in: Maddala, G.S., Phillips, P.C.B., Srinivasan, T.N. (Eds.), Advances in Econometrics and Quantitative Econometrics. Basil Blackwell, Oxford.
32. Newey, W.K., West, K.D., 1987. A simple positive-definite, heteroskedastic and autocorrelation consistent covariance matrix. Econometrica 55, 703-708.
33. Nychka, D., Ellner, S., Gallant, A.R., McCaffrey, D., 1992. Finding chaos in noisy systems. Journal of the Royal Statistical Society, Series B 54, 399-426.
34. Ouliaris, S., Phillips, P.C.B., 1994. COINT 2.0: Gauss procedures for cointegrated regressions. Predicta Software Inc, 133 Concord Drive, Madison CT 06443.
35. Robinson, P.M., 1983. Nonparametric estimators for time series. Journal of Time Series Analysis 4, 185-208.
36. Tong, H., 1990. Non-linear Time Series: A Dynamical Systems Approach. Clarendon Press, Oxford.
37. Watson, G.S., 1954. Extreme values in samples from m-dependent stationary stochastic processes. The Annals of Mathematical Statistics 25, 798-800.
38. White, H., 1984. Asymptotic Theory for Econometricians. Academic Press, New York.