Complexity Analysis of Time Series Based on Generalized Fractional Order Refined Composite Multiscale Dispersion Entropy

2020 ◽  
Vol 30 (14) ◽  
pp. 2050211
Author(s):  
Yu Wang ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Fractional Order ◽  
Complexity Analysis ◽  
Financial Time Series ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Entropy Model ◽  
Intrinsic Nature ◽  
New Models ◽  
Stability And Accuracy

Based on the dispersion entropy model, combined with multiscale analysis method and fractional order information entropy theory, this paper proposes new models — the generalized fractional order multiscale dispersion entropy (GMDE) and the generalized fractional order refined composite multiscale dispersion entropy (GRCMDE). The new models take the amplitude value information of the sequence itself into consideration, which can make better use of some key information in the sequence and have a higher stability and accuracy. In addition, extending the algorithm to generalized fractional order can make the model better capture the small evolution of the signal data, which is more advantageous for studying the dynamic characteristics of complex systems. This paper verifies the effectiveness of the new models by combining theoretical analysis with empirical research, and further studies the complexity of the financial system and the nature of its multiple time scales. The results show that the proposed GMDE, GRCMDE can better detect the intrinsic nature of financial time series and can distinguish the financial market complexity of different countries.

scholarly journals Quantifying the Multiscale Predictability of Financial Time Series by an Information-Theoretic Approach

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 684 ◽  
Author(s):  
Xiaojun Zhao ◽  
Chenxu Liang ◽  
Na Zhang ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
High Frequency ◽  
Stock Price ◽  
Financial Time Series ◽  
High Frequency Data ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Information Theoretic ◽  
Daily Data ◽  
Wide Range

Making predictions on the dynamics of time series of a system is a very interesting topic. A fundamental prerequisite of this work is to evaluate the predictability of the system over a wide range of time. In this paper, we propose an information-theoretic tool, multiscale entropy difference (MED), to evaluate the predictability of nonlinear financial time series on multiple time scales. We discuss the predictability of the isolated system and open systems, respectively. Evidence from the analysis of the logistic map, Hénon map, and the Lorenz system manifests that the MED method is accurate, robust, and has a wide range of applications. We apply the new method to five-minute high-frequency data and the daily data of Chinese stock markets. Results show that the logarithmic change of stock price (logarithmic return) has a lower possibility of being predicted than the volatility. The logarithmic change of trading volume contributes significantly to the prediction of the logarithmic change of stock price on multiple time scales. The daily data are found to have a larger possibility of being predicted than the five-minute high-frequency data. This indicates that the arbitrage opportunity exists in the Chinese stock markets, which thus cannot be approximated by the effective market hypothesis (EMH).

scholarly journals Cardiovascular and Cardiorespiratory Signals Complexity Analysis Using Different Techniques

2021 ◽  
Author(s):  
Kirti Singh ◽  
Indu Saini ◽  
Neetu Sood
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Complexity Analysis ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Short Term ◽  
Dynamic Complexity ◽  
Long Range Correlations ◽  
Biological Time

In recent decades, the concept of complex physiological systems has become more and more popular. The evaluation of the biological time series' dynamic complexity is an essential subject with possible applications such as the characterization of physiological states i.e. HRV, BP, and RESP signals and pathological disorders to the measurement of diagnostic parameters. The convergence of several physiological regulation processes is the cause of heterogeneity in cardiovascular time series, that consider many factors and function over several time scales, resulting not only the presence of short-term dynamics but also the coexistence of long-range correlations in various physiological signals. The most popular approach to evaluating the dynamic complexity and irregularity of time series over multiple time scales is entropy based analysis. The most used approach is multiscale entropy (MSE) and refined MSE (RMSE). It is then added to the heart period time series, respiration time series, and blood pressure time series, measured in young subjects and old subjects under resting conditions. This research applies to short-term cardiovascular and cardiorespiratory variability documents that LMSE can better describe physiological processes' behavior causing biological oscillations at various time scales than RMSE.

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

Wavelet Entropy Energy Measure (WEEM): A multiscale measure to grade a geophysical system's predictability

2021 ◽  
Author(s):  
Ravi Kumar Guntu ◽  
Ankit Agarwal
Keyword(s):  
Time Series ◽  
Energy Distribution ◽  
Energy Concentration ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Wavelet Entropy ◽  
Wavelet Energy ◽  
Energy Measure ◽  
Geophysical Time Series ◽  
Geophysical System

<p>Model-free gradation of predictability of a geophysical system is essential to quantify how much inherent information is contained within the system and evaluate different forecasting methods' performance to get the best possible prediction. We conjecture that Multiscale Information enclosed in a given geophysical time series is the only input source for any forecast model. In the literature, established entropic measures dealing with grading the predictability of a time series at multiple time scales are limited. Therefore, we need an additional measure to quantify the information at multiple time scales, thereby grading the predictability level. This study introduces a novel measure, Wavelet Entropy Energy Measure (WEEM), based on Wavelet entropy to investigate a time series's energy distribution. From the WEEM analysis, predictability can be graded low to high. The difference between the entropy of a wavelet energy distribution of a time series and entropy of wavelet energy of white noise is the basis for gradation. The metric quantifies the proportion of the deterministic component of a time series in terms of energy concentration, and its range varies from zero to one. One corresponds to high predictable due to its high energy concentration and zero representing a process similar to the white noise process having scattered energy distribution. The proposed metric is normalized, handles non-stationarity, independent of the length of the data. Therefore, it can explain the evolution of predictability for any geophysical time series (ex: precipitation, streamflow, paleoclimate series) from past to the present. WEEM metric's performance can guide the forecasting models in getting the best possible prediction of a geophysical system by comparing different methods. </p>

scholarly journals Warming and Weakening of the Abyssal Flow through Samoan Passage

2016 ◽  
Vol 46 (8) ◽  
pp. 2389-2401 ◽  
Author(s):  
Gunnar Voet ◽  
Matthew H. Alford ◽  
James B. Girton ◽  
Glenn S. Carter ◽  
John B. Mickett ◽  
...  
Keyword(s):  
Time Series ◽  
North Pacific ◽  
Volume Transport ◽  
Meridional Overturning Circulation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Confidence Limits ◽  
The North ◽  
Meridional Overturning ◽  
Flow Through

AbstractThe abyssal flow of water through the Samoan Passage accounts for the majority of the bottom water renewal in the North Pacific, thereby making it an important element of the meridional overturning circulation. Here the authors report recent measurements of the flow of dense waters of Antarctic and North Atlantic origin through the Samoan Passage. A 15-month long moored time series of velocity and temperature of the abyssal flow was recorded between 2012 and 2013. This allows for an update of the only prior volume transport time series from the Samoan Passage from WOCE moored measurements between 1992 and 1994. While highly variable on multiple time scales, the overall pattern of the abyssal flow through the Samoan Passage was remarkably steady. The time-mean northward volume transport of about 5.4 Sv (1 Sv ≡ 106 m3 s−1) in 2012/13 was reduced compared to 6.0 Sv measured between 1992 and 1994. This volume transport reduction is significant within 68% confidence limits (±0.4 Sv) but not at 95% confidence limits (±0.6 Sv). In agreement with recent studies of the abyssal Pacific, the bottom flow through the Samoan Passage warmed significantly on average by 1 × 10−3°C yr−1 over the past two decades, as observed both in moored and shipboard hydrographic observations. While the warming reflects the recently observed increasing role of the deep oceans for heat uptake, decreasing flow through Samoan Passage may indicate a future weakening of this trend for the abyssal North Pacific.

MULTIPLE TIME-SCALES NONLINEAR PREDICTION OF RIVER FLOW USING CHAOS APPROACH

2016 ◽  
Vol 78 (7) ◽  
Author(s):  
Nur Hamiza Adenan ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Time Series ◽  
Time Scales ◽  
River Flow ◽  
Moving Average ◽  
Multiple Time Scales ◽  
Support Vector ◽  
Multiple Time ◽  
Nonlinear Prediction ◽  
Prediction Result ◽  
Flow Prediction

River flow prediction is important in determining the amount of water in certain areas to ensure sufficient water resources to meet the demand. Hence, an analysis and prediction of multiple time-scales data for daily, weekly and 10-day averaged time series were performed using chaos approach. An analysis was conducted at the Tanjung Tualang station, Malaysia. This method involved the reconstruction of a single variable in a multi-dimensional phase space. River flow prediction was performed using local linear approximation. The prediction result is close to agreement with a high correlation coefficient for each time scale. The analysis suggests that the presence of low dimensional chaos as an optimal embedding dimension exists when the inverse method is adopted. In addition, a comparison of the prediction performance of chaos approach, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), support vector machine (SVM) and least squares support vector machines (LSSVM) were performed. The comparative analysis shows that all methods provide comparable predictions. However, chaos approach provides a simpler means of analysis since it only use a scalar time series (river flow data). Therefore, the relevant authorities may use this prediction result for the creation of a water management system for local benefit.

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