scholarly journals Complex Network Construction of Univariate Chaotic Time Series Based on Maximum Mean Discrepancy

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 142
Author(s):  
Jiancheng Sun
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Gaussian Mixture ◽  
Chaotic Time Series ◽  
Network Construction ◽  
Maximum Mean Discrepancy ◽  
Univariate Time Series ◽  
Dimensional Phase Space ◽  
The Common ◽  
The Lorenz System

The analysis of chaotic time series is usually a challenging task due to its complexity. In this communication, a method of complex network construction is proposed for univariate chaotic time series, which provides a novel way to analyze time series. In the process of complex network construction, how to measure the similarity between the time series is a key problem to be solved. Due to the complexity of chaotic systems, the common metrics is hard to measure the similarity. Consequently, the proposed method first transforms univariate time series into high-dimensional phase space to increase its information, then uses Gaussian mixture model (GMM) to represent time series, and finally introduces maximum mean discrepancy (MMD) to measure the similarity between GMMs. The Lorenz system is used to validate the correctness and effectiveness of the proposed method for measuring the similarity.

Finding Hidden Communities in Complex Networks from Chaotic Time Series

2016 ◽  
Vol 3 (2) ◽  
pp. 350
Author(s):  
Jiancheng Sun
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Complex Network ◽  
Chaotic Time Series ◽  
Topology Structure ◽  
Complex Network Theory ◽  
Single Vertex ◽  
Reconstructed Phase Space ◽  
Information Coefficient ◽  
Maximal Information Coefficient

Recent works show that complex network theory may be another powerful tool in time series analysis. In this paper, we construct complex networks from the chaotic time series with Maximal Information Coefficient (MIC). Each vector point in the reconstructed phase space is represented by a single vertex and edge determined by MIC. By using the Chua’s circuit system, we illustrate the potential of these complex network measures for the detection of the topology structure of the network. Comparing with the linear relationship measure, we find that the topology structure of the community with MIC reveals the hidden or implied correlation of the network.

scholarly journals Construction of complex networks from time series based on the cross correlation interval

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 253-260 ◽  
Author(s):  
Chen Feng ◽  
Bo He
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Complex Network ◽  
Cross Correlation ◽  
Clustering Coefficient ◽  
Two Phase ◽  
Correlation Interval ◽  
The Cross ◽  
The Lorenz System ◽  
Dynamic States

AbstractIn this paper, a new approach to map time series into complex networks based on the cross correlation interval is proposed for the analysis of dynamic states of time series on different scales. In the proposed approach, a time series is divided into time series segments and each segment is reconstructed to a phase space defined as a node of the complex network. The cross correlation interval, which characterizes the degree of correlation between two phase spaces, is computed as the distance between the two nodes. The clustering coefficient and efficiency are used to determine an appropriate threshold for the construction of a complex network that can effectively describe the dynamic states of a complex system. In order to verify the efficiency of the proposed approach, complex networks are constructed for time series generated from the Lorenz system, for white Gaussian noise time series and for sea clutter time series. The experimental results have demonstrated that nodes in different communities represent different dynamic states . Therefore, the proposed approach can be used to uncover the dynamic characteristics of the complex systems.

scholarly journals A Gaussian Mixture Autoregressive Model for Univariate Time Series

2014 ◽  
Vol 36 (2) ◽  
pp. 247-266 ◽  
Author(s):  
Leena Kalliovirta ◽  
Mika Meitz ◽  
Pentti Saikkonen
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Gaussian Mixture ◽  
Univariate Time Series

scholarly journals Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Liyun Su ◽  
Chenlong Li
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaos Theory ◽  
Nearest Neighbor ◽  
Simulated Data ◽  
Real Data ◽  
Chaotic Time Series ◽  
Dimensional Phase Space ◽  
Local Functional ◽  
Functional Coefficient

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed inm-dimensional phase space with a time delayτby using chaos theory. Secondly, select the nearest neighbor points by using local method in them-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.

Complex Network Construction of Multivariate Time Series Using Information Geometry

2019 ◽  
Vol 49 (1) ◽  
pp. 107-122 ◽  
Author(s):  
Jiancheng Sun ◽  
Yong Yang ◽  
Neal N. Xiong ◽  
Liyun Dai ◽  
Xiangdong Peng ◽  
...  
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Multivariate Time Series ◽  
Information Geometry ◽  
Network Construction

scholarly journals Latent Network Construction for Univariate Time Series Based on Variational Auto-Encode

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1071
Author(s):  
Jiancheng Sun ◽  
Zhinan Wu ◽  
Si Chen ◽  
Huimin Niu ◽  
Zongqing Tu
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Statistical Manifold ◽  
Multivariate Gaussian Distribution ◽  
Gaussian Distributions ◽  
Network Construction ◽  
Univariate Time Series ◽  
Analyze Time Series ◽  
Important Branch ◽  
Original Information

Time series analysis has been an important branch of information processing, and the conversion of time series into complex networks provides a new means to understand and analyze time series. In this work, using Variational Auto-Encode (VAE), we explored the construction of latent networks for univariate time series. We first trained the VAE to obtain the space of latent probability distributions of the time series and then decomposed the multivariate Gaussian distribution into multiple univariate Gaussian distributions. By measuring the distance between univariate Gaussian distributions on a statistical manifold, the latent network construction was finally achieved. The experimental results show that the latent network can effectively retain the original information of the time series and provide a new data structure for the downstream tasks.

A COMPARATIVE STUDY BETWEEN UNIVARIATE AND BIVARIATE TIME SERIES MODELS FOR CRUDE PALM OIL INDUSTRY IN PENINSULAR MALAYSIA

2020 ◽  
Vol 5 (1) ◽  
pp. 374
Author(s):  
Pauline Jin Wee Mah ◽  
Nur Nadhirah Nanyan
Keyword(s):  
Time Series ◽  
Palm Oil ◽  
Moving Average ◽  
Forecast Accuracy ◽  
Peninsular Malaysia ◽  
Time Series Models ◽  
Crude Palm Oil ◽  
Univariate Time Series ◽  
Import And Export ◽  
Bivariate Time Series

The main purpose of this study is to compare the performances of univariate and bivariate models on four time series variables of the crude palm oil industry in Peninsular Malaysia. The monthly data for the four variables, which are the crude palm oil production, price, import and export, were obtained from Malaysian Palm Oil Board (MPOB) and Malaysian Palm Oil Council (MPOC). In the first part of this study, univariate time series models, namely, the autoregressive integrated moving average (ARIMA), fractionally integrated autoregressive moving average (ARFIMA) and autoregressive autoregressive (ARAR) algorithm were used for modelling and forecasting purposes. Subsequently, the dependence between any two of the four variables were checked using the residuals’ sample cross correlation functions before modelling the bivariate time series. In order to model the bivariate time series and make prediction, the transfer function models were used. The forecast accuracy criteria used to evaluate the performances of the models were the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The results of the univariate time series showed that the best model for predicting the production was ARIMA  while the ARAR algorithm were the best forecast models for predicting both the import and export of crude palm oil. However, ARIMA  appeared to be the best forecast model for price based on the MAE and MAPE values while ARFIMA  emerged the best model based on the RMSE value.  When considering bivariate time series models, the production was dependent on import while the export was dependent on either price or import. The results showed that the bivariate models had better performance compared to the univariate models for production and export of crude palm oil based on the forecast accuracy criteria used.

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