Chaos detection in economics. Metric versus topological tools
In their paper Frank F., Gencay R., and Stengos T., (1988) analyze the quarterly macroeconomic data from 1960 to 1988 for West Germany, Italy, Japan and England. The goal was to check for the presence of deterministic chaos. To ensure that the data analysed was stationary they used a first difference then tried a linear fit. Using a reasonable AR specification for each time series their conclusion was that time series showed different structures. In particular the non linear structure was present in the time series of Japan. Nevertheless the application of metric tools for detecting chaos (correlation dimension and Lyapunov exponent) didn’t show presence of chaos in any time series. Starting from this conclusion we applied a topological tool Visual Recurrence Analysis to these time series to compare the results. The purpose is to verify if the analysis performed by a topological tool could give results different from ones obtained using a metric tool.
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- Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, EconWPA.
- Jorge Belaire-Franch, & Dulce Contreras & Lorena Tordera-Lledo, 2002. "Assessing Non-Linear Structures in Real Exchange Rates Using Recurrence Plot Strategies," Computing in Economics and Finance 2002 239, Society for Computational Economics.
- Gilmore, Claire G., 1993. "A new test for chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 209-237, October.
- McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
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