1995/10/25 by Melvin Leok Boon Tiong, Tiong, Melvin Leok Boon
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Chaos control and synchronization #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.chao-dyn/9510015
The correlation dimension and limit capacity serve theoretically as lower and upper bounds, respectively, of the fractal dimension of attractors of dynamic systems. In this paper, we show that estimates of the correlation dimension grow rapidly with increasing noise level in the time-series, while estimates of the limit capacity remain relatively unaffected. It is therefore proposed that the limit capacity be used in studies of noisy data, despite its heavier computational requirements. An analysis of Singapore wind data with the limit capacity estimate revealed a surprisingly low dimension (~2.5). It is suggested that further studies be made with comprehensive equatorial weather data.