A Formalism for the Dimensional Analysis of Time Series
The possibility that low dimensional chaotic systems generate stochastic dynamics is now a standard idea in economics. As a consequence, modern time series analysis has among its primary goals the design and computer implementation of techniques for distinguishing complex deterministic dynamics from purely random processes. It is essential here to have some notion of dimension, since stochastic processes are considered high dimensional whereas interesting chaotic systems low. However, a well founded interpretation of the analysis is not available when the data have not been observed along an orbit of a smooth dynamical system, which is not plausible in economic time series. I propose a formalism for the rigorous analysis of dimension of scalar data monitored in any dynamical process, deterministic or stochastic. The formalism provides an interpretation of the dimensional analysis of ergodic processes while retaining the meaning of the classical dimensional test for the detection of chaos. We also show some applications to financial data.
|Date of creation:||01 Mar 1999|
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- Liu, T & Granger, C W J & Heller, W P, 1992. "Using the Correlation Exponent to Decide whether an Economic Series is Chaotic," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S25-39, Suppl. De.
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