On Nonlinear, Stochastic Dynamics in Economic and Financial Time Series
The search for deterministic chaos in economic and financial time series has attracted much interest over the past decade. Evidence of chaotic structures is usually blurred, however, by large random components in the time series. In the first part of this paper, a sophisticated algorithm for estimating the largest Lyapunov exponent with confidence intervals is applied to artificially generated and real-world time series. Although the possibility of testing empirically for positivity of the estimated largest Lyapunov exponent is an advantage over other existing methods, the interpretability of the obtained results remains problematic. For instance, it is practically impossible to distinguish chaotic and periodic dynamics in the presence of dynamical noise even for simple dynamical systems. We conclude that the notion of sensitive dependence on initial conditions, as it has been developed for deterministic dynamics, can hardly be transferred into a stochastic context. Therefore, the second part of the paper aims to measure the dependencies of stochastic dynamics on the basis of a distributional characterization of the dynamics. For instance, the dynamics of financial return series are essentially captured by heteroskedastic models. We adopt a sensitivity measure proposed in literature and derive analytical expressions for the most important classes of stochastic dynamics. In practice, the sensitivity measure for the a priori unknown dynamics of a system can be calculated after estimating the conditional density of the system's state variable.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 4 (2000)
Issue (Month): 3 (October)
|Contact details of provider:|| Web page: https://www.degruyter.com|
|Order Information:||Web: https://www.degruyter.com/view/j/snde|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
- Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
- Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:4:y:2000:i:3:n:2. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.