A Cross-Reference Method for Nonlinear Time Series Analysis in Semi-Blind Case

In this paper, we propose a cross reference method for nonlinear time series analyzing in semi blind case, that is, the dynamic equations modeling the time series are known but the corresponding parameters are not. The tasks of noise reduction and parameter estimation which were fulfilled separately before are combined iteratively. With the positive interaction between the two processing modules, the method is somewhat superior. Some prior work can be viewed as special cases of this general framework. The simulations for noise reduction and parameter estimation of contaminated chaotic time series show improved performance of our method compared with previous work.

Nonlinear Analysis of Physiological Time Series

The heart rate variability could be explained by a low-dimensional governing mechanism. There has been increasing interest in verifying and understanding the coupling between the respiration and the heart rate. In this paper we use the nonlinear detection method to detect the nonlinear deterministic component in the physiological time series by a single variable series and two variables series respectively, and use the conditional information entropy to analyze the correlation between the heart rate, the respiration and the blood oxygen concentration. The conclusions are that there is the nonlinear deterministic component in the heart rate data and respiration data, and the heart rate and the respiration are two variables originating from the same underlying dynamics.

Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES

The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man＇s participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay r by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D; Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of Poincare map, and the non-circle degree Dnc and non-order degree Dno of quasi-phase orbit. Chaos features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.

Small-time scale network traffic prediction based on a local support vector machine regression model

In this paper we apply the nonlinear time series analysis method to small-time scale traffic measurement data. The prediction-based method is used to determine the embedding dimension of the traffic data. Based on the reconstructed phase space, the local support vector machine prediction method is used to predict the traffic measurement data, and the BIC-based neighbouring point selection method is used to choose the number of the nearest neighbouring points for the local support vector machine regression model. The experimental results show that the local support vector machine prediction method whose neighbouring points are optimized can effectively predict the small-time scale traffic measurement data and can reproduce the statistical features of real traffic measurements.

Cross and joint ordinal partition transition networks for multivariate time series analysis

We propose the construction of cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is a prototypical scenario in dynamical systems. We systematically show that cross and joint ordinal pattern transition networks are sensitive to phase synchronization. Furthermore, we find that some particular missing ordinal patterns play crucial roles in forming the detailed structures in the parameter space, whereas the calculations of permutation entropy measures often do not. We conclude that cross and joint ordinal partition transition network approaches provide complementary insights into the traditional symbolic analysis of synchronization transitions.

Monthly and seasonal streamflow forecasting of large dryland catchments in Brazil

Streamflow forecasting in drylands is challenging.Data are scarce,catchments are highly humanmodified and streamflow exhibits strong nonlinear responses to rainfall.The goal of this study was to evaluate the monthly and seasonal streamflow forecasting in two large catchments in the Jaguaribe River Basin in the Brazilian semi-arid area.We adopted four different lead times:one month ahead for monthly scale and two,three and four months ahead for seasonal scale.The gaps of the historic streamflow series were filled up by using rainfall-runoff modelling.Then,time series model techniques were applied,i.e.,the locally constant,the locally averaged,the k-nearest-neighbours algorithm(k-NN)and the autoregressive(AR)model.The criterion of reliability of the validation results is that the forecast is more skillful than streamflow climatology.Our approach outperformed the streamflow climatology for all monthly streamflows.On average,the former was 25%better than the latter.The seasonal streamflow forecasting(SSF)was also reliable(on average,20%better than the climatology),failing slightly only for the high flow season of one catchment(6%worse than the climatology).Considering an uncertainty envelope(probabilistic forecasting),which was considerably narrower than the data standard deviation,the streamflow forecasting performance increased by about 50%at both scales.The forecast errors were mainly driven by the streamflow intra-seasonality at monthly scale,while they were by the forecast lead time at seasonal scale.The best-fit and worst-fit time series model were the k-NN approach and the AR model,respectively.The rainfall-runoff modelling outputs played an important role in improving streamflow forecasting for one streamgauge that showed 35%of data gaps.The developed data-driven approach is mathematical and computationally very simple,demands few resources to accomplish its operational implementation and is applicable to other dryland watersheds.Our findings may be part of drought forecasting systems and potentially help allocating water months in advance.Moreover,the developed strategy can serve as a baseline for more complex streamflow forecast systems.