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Correlation Dimension (correlation + dimension)
Selected AbstractsChaotic analysis of predictability versus knowledge discovery techniques: case study of the Polish stock marketEXPERT SYSTEMS, Issue 5 2002Hak Chun Increasing evidence over the past decade indicates that financial markets exhibit nonlinear dynamics in the form of chaotic behavior. Traditionally, the prediction of stock markets has relied on statistical methods including multivariate statistical methods, autoregressive integrated moving average models and autoregressive conditional heteroskedasticity models. In recent years, neural networks and other knowledge techniques have been applied extensively to the task of predicting financial variables. This paper examines the relationship between chaotic models and learning techniques. In particular, chaotic analysis indicates the upper limits of predictability for a time series. The learning techniques involve neural networks and case,based reasoning. The chaotic models take the form of R/S analysis to measure persistence in a time series, the correlation dimension to encapsulate system complexity, and Lyapunov exponents to indicate predictive horizons. The concepts are illustrated in the context of a major emerging market, namely the Polish stock market. [source] A comprehensive approach to characterization of the nonlinearity of runoff in the headwaters of the Tarim River, western ChinaHYDROLOGICAL PROCESSES, Issue 2 2010Jianhua Xu Abstract Nonlinear characteristics of the runoff processes in the headwaters of the Tarim River were identified and evaluated using several selected methods, including wavelet analysis, correlation dimension, and R/S analysis. Time-series of annual data describing runoff, average temperature, and precipitation from 1957 to 2005 were used to construct and test empirical models. The primary findings of this study were as follows: (1) The annual runoff of the headwaters are complex and nonlinear in nature, and they each presented periodic, nonlinear trends at the chosen time scales, chaotic dynamics, and long-memory characteristics. (2) These nonlinear trends appeared to have resulted from the regional climatic changes that occurred during the study period. The periodicity of changes in runoff occurred on an approximately 25-year cycle, which appeared to be correlated with temperature and precipitation cycles. In addition, the annual runoff exhibited a significant, positive correlation with the temperature and precipitation factors at the 4-, 8-, 16-, and 32-year temporal scales. (3) The correlation dimensions of the attractor derived from the runoff time series for the Hotan, Yarkand, and Aksu rivers were all greater than 3·0 and non-integral, implying that all three rivers are dynamic chaotic systems that are sensitive to initial conditions, and that the dynamic modelling of their annual runoff requires at least four independent variables. (4) The computed Hurst exponents indicate that a long-term memory characteristic exists in the annual runoff processes. However, there were some differences observed, with the Aksu and Yarkand rivers demonstrating a persistent trait, and the Hotan River exhibiting an anti-persistent feature. Copyright © 2009 John Wiley & Sons, Ltd. [source] Isolating the root cause of propagated oscillations in process plantsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2005Xiaoyun Zang Abstract Oscillations are a common type of propagated disturbance, whose sources might be attributable to a number of different phenomena such as poor controller tuning or actuator nonlinearity. A number of data-driven methods have already been proposed to isolate the source loop of nonlinearity induced plant-wide oscillations. Amongst these the bi-amplitude ratio index, correlation dimension, maximal Lyapunov exponent, nonlinearity index and spectral ICA show promise. The propagation of oscillations is first examined in order to gain an understanding of how this might affect the performances of the various techniques. The various methods are then described and their performance on a set of simulation generated data and two industrial case studies are compared. Copyright © 2004 John Wiley & Sons, Ltd. [source] CHAOTIC FORECASTING OF DISCHARGE TIME SERIES: A CASE STUDY,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 2 2001Francesco Lisi ABSTRACT: This paper considers the problem of forecasting the discharge time series of a river by means of a chaotic approach. To this aim, we first check for some evidence of chaotic behavior in the dynamic by considering a set of different procedures, namely, the phase portrait of the attractor, the correlation dimension, and the largest Lyapunov exponent. Their joint application seems to confirm the presence of a nonlinear deterministic dynamic of chaotic type. Second, we consider the so-called nearest neighbors predictor and we compare it with a classical linear model. By comparing these two predictors, it seems that nonlinear river flow modeling, and in particular chaotic modeling, is an effective method to improve predictions. [source] Large-scale cosmic homogeneity from a multifractal analysis of the PSCz catalogueMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2000Jun Pan We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSCz sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D2=2.992±0.003 for r>30 h,1 Mpc. This provides strong evidence in favour of a universe that obeys the cosmological principle. [source] A Comparison of Flow Dynamics and Flow Structure in a Riser and a DownerCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 4 2007B. Wu Abstract Flow development and flow dynamics were systematically investigated using local solids concentration measurements in a pair consisting of a downer (0.1,m I.D., 9.3,m high) and a riser of the same diameter (0.1,m I.D., 15.1,m high). Both statistical and chaos analysis were employed. Values for the Kolmogorov entropy (K), correlation dimension (D), and Hurst exponent (H) were estimated from time series of solids concentration measurements. Axial distributions of chaos parameters were more complex in the downer than those in the riser, especially in the entrance section. Flow in the downer was more uniform with a flatter core in all the radial profiles of chaos parameters. The radial profiles of K varied significantly with increasing axial levels due to different clustering behavior in the wall region of the downer. In both the riser and the downer, anti-persistent flow in the core region and persistent flow behavior near the wall were identified from the profiles of H. Different flow behavior in the region close to the wall in the downer and riser was characterized from the combination of the three chaos parameters. Relationships between chaos parameters and local time-averaged solids holdup in the core and wall regions of the developed sections in both the downer and riser were also analyzed. [source] Nonlinear determinism in river flow: prediction as a possible indicatorEARTH SURFACE PROCESSES AND LANDFORMS, Issue 7 2007Bellie SivakumarArticle first published online: 6 DEC 200 Abstract Whether or not river flow exhibits nonlinear determinism remains an unresolved question. While studies on the use of nonlinear deterministic methods for modeling and prediction of river flow series are on the rise and the outcomes are encouraging, suspicions and criticisms of such studies continue to exist as well. An important reason for this situation is that the correlation dimension method, used as a nonlinear determinism identification tool in most of those studies, may possess certain limitations when applied to real river flow series, which are always finite and often short and also contaminated with noise (e.g. measurement error). In view of this, the present study addresses the issue of nonlinear determinism in river flow series using prediction as a possible indicator. This is done by (1) reviewing studies that have employed nonlinear deterministic methods (coupling phase-space reconstruction and local approximation techniques) for river flow predictions and (2) identifying nonlinear determinism (or linear stochasticity) based on the level of prediction accuracy in general, and on the prediction accuracy against the phase-space reconstruction parameters in particular (termed as the ,inverse approach'). The results not only provide possible indications to the presence of nonlinear determinism in the river flow series studied, but also support, both qualitatively and quantitatively, the low correlation dimensions reported for such. Therefore, nonlinear deterministic methods are a viable complement to linear stochastic ones for studying river flow dynamics, if sufficient caution is exercised in their applications and in interpreting the outcomes. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||