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.

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

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.

scholarly journals Evaluation of Multi-Precipitation Products for Multi-Time Scales and Spatial Distribution During 2007-2015

2019 ◽  
Vol 5 (1) ◽  
pp. 255 ◽  
Author(s):  
Nguyen Tien Thanh
Keyword(s):  
Time Series ◽  
Spatial Distribution ◽  
Water Resources ◽  
Time Scales ◽  
Heavy Rain ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Precipitation Estimates ◽  
Rain Events ◽  
Trmm 3B42

Recently, several precipitation products are released with the improved algorithm to strengthen the performance of precipitation construction and monitoring. These data play a key role in a wide range of hydrological models, water resources modeling and environmental researches. Especially in developing countries like Vietnam, it is challenging to gather data for long-term time series at scales of daily and sub-daily due to the very coarse density of observation station. In order to overcome the problem of data scarcity, this study aims to evaluate the performance of newest multiple precipitation products including Tropical Rainfall Measuring Mission (TRMM 3B42 V7), Climate Prediction Center (CPC) MORPHing Version 1.0 (CMORPH_V1.0), European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis systems (ERA-Interim), Climate Research Unit Time series Version 4.0.1 (CRU TS 4.0.1) and Asian Precipitation-Highly-Resolved Observational Data Integration Towards Evaluation of Water Resources version 2 (APHRODITE) in comparison with measured precipitation for multiple time scales (daily, monthly, seasonal and annual), taking the VuGia-ThuBon (VG-TB) as a pilot basin where climate regime is complex. Seven continuous and four dichotomous statistics are applied to evaluate the precipitation estimates qualitatively at multiple time scales. In addition, specifically, evaluation of spatial distribution of multiple time scales is implemented. The results show lower precipitation estimates in areas of high elevation and higher precipitation estimates over the areas of plain and coastal in comparison with measured precipitation for all considered precipitation data. More importantly, ERA-Interim well captures rain events of heavy rain (50.0-100 mm/day). CMORHPH_V1.0 better reproduces the rain events with little overestimation of light rain (0.6-6 mm/day) than the others. For zero rain events (0-0.6 mm/day), TRMM 3B42 V7 gives the best performance. Furthermore, the cumulative distribution function of APHRODITE well matches the distribution of measured precipitation. All precipitation products completely fail to capture the rain events of extremely heavy rain. More importantly, a formula is proposed to scale and adjust the merged satellite precipitation at a sub-daily scale.

scholarly journals STFT-LDA: An algorithm to facilitate the visual analysis of building seismic responses

2021 ◽  
pp. 147387162110386
Author(s):  
Zhenge Zhao ◽  
Danilo Motta ◽  
Matthew Berger ◽  
Joshua A Levine ◽  
Ismail B Kuzucu ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Visual Analysis ◽  
Time Series Data ◽  
Series Data ◽  
Multiple Time Scales ◽  
Prototype System ◽  
Multiple Time ◽  
Seismic Responses ◽  
Large Ensembles

Civil engineers use numerical simulations of a building’s responses to seismic forces to understand the nature of building failures, the limitations of building codes, and how to determine the latter to prevent the former. Such simulations generate large ensembles of multivariate, multiattribute time series. Comprehensive understanding of this data requires techniques that support the multivariate nature of the time series and can compare behaviors that are both periodic and non-periodic across multiple time scales and multiple time series themselves. In this paper, we present a novel technique to extract such patterns from time series generated from simulations of seismic responses. The core of our approach is the use of topic modeling, where topics correspond to interpretable and discriminative features of the earthquakes. We transform the raw time series data into a time series of topics, and use this visual summary to compare temporal patterns in earthquakes, query earthquakes via the topics across arbitrary time scales, and enable details on demand by linking the topic visualization with the original earthquake data. We show, through a surrogate task and an expert study, that this technique allows analysts to more easily identify recurring patterns in such time series. By integrating this technique in a prototype system, we show how it enables novel forms of visual interaction.

TREND FILTERING: EMPIRICAL MODE DECOMPOSITIONS VERSUS ℓ1 AND HODRICK–PRESCOTT

2011 ◽  
Vol 03 (01n02) ◽  
pp. 41-61 ◽  
Author(s):  
AZADEH MOGHTADERI ◽  
PIERRE BORGNAT ◽  
PATRICK FLANDRIN
Keyword(s):  
Time Series ◽  
Arbitrary Shape ◽  
Low Frequency ◽  
Data Driven ◽  
Intrinsic Mode Functions ◽  
Novel Approach ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Estimation Parameters ◽  
Simulated Time Series

Considering the problem of extracting a trend from a time series, we propose a novel approach based on empirical mode decomposition (EMD), called EMD trend filtering. The rationale is that EMD is a completely data-driven technique, which offers the possibility of estimating a trend of arbitrary shape as a sum of low-frequency intrinsic mode functions produced by the EMD. Based on an empirical analysis of EMD, an automatic procedure is proposed to select the requisite intrinsic mode functions. The performance of the EMD trend filtering is evaluated on simulated time series containing different forms of trends. Comparing furthermore to two existing techniques (ℓ1-trend filtering and Hodrick–Prescott filtering), we observe that the EMD trend filtering performs very similarly, while it does not require assumptions on the form of the trend and it is free from estimation parameters. We also illustrate the performance of the technique on the S&P 500 index, as an example of real-world time series.

scholarly journals Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 315 ◽  
Author(s):  
Aurora Martins ◽  
Riccardo Pernice ◽  
Celestino Amado ◽  
Ana Paula Rocha ◽  
Maria Eduarda Silva ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Scales ◽  
Multivariate Time Series ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Control Mechanisms ◽  
Long Range Correlations ◽  
Dynamical Complexity

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

scholarly journals A Novel Phase Space Reconstruction- (PSR-) Based Predictive Algorithm to Forecast Atmospheric Particulate Matter Concentration

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Syed Ahsin Ali Shah ◽  
Wajid Aziz ◽  
Malik Sajjad Ahmed Nadeem ◽  
Majid Almaraashi ◽  
Seong-O. Shim ◽  
...  
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Particulate Matter ◽  
Phase Space ◽  
Time Scales ◽  
Atmospheric Particulate Matter ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Atmospheric Particulate ◽  
Mass Concentrations

The prediction of atmospheric particulate matter (APM) concentration is essential to reduce adverse effects on human health and to enforce emission restrictions. The dynamics of APM are inherently nonlinear and chaotic. Phase space reconstruction (PSR) is one of the widely used methods for chaotic time series analysis. The APM mass concentrations are an outcome of complex anthropogenic contributors evolving with time, which may operate on multiple time scales. Thus, the traditional single-variable PSR-based prediction algorithm in which data points of last embedding dimension are used as a target set may fail to account for multiple time scales inherent in APM concentrations. To address this issue, we propose a novel PSR-based scientific solution that accounts for the information contained at multiple time scales. Different machine learning algorithms are used to evaluate the performance of the proposed and traditional PSR techniques for predicting mass concentrations of particulate matter up to 2.5 micron (PM2.5), up to 10 micron (PM10.0), and ratio of PM2.5/PM10.0. Hourly time series data of PM2.5 and PM10.0 mass concentrations are collected from January 2014 to September 2015 at the Masfalah air quality monitoring station (couple of kilometers from the Holy Mosque in Makkah, Saudi Arabia). The performances of various learning algorithms are evaluated using RMSE and MAE. The results demonstrated that prediction error of all the machine learning techniques is smaller for the proposed PSR approach compared to traditional approach. For PM2.5, FFNN leads to best results (both RMSE and MAE 0.04 μgm−3), followed by SVR-L (RMSE 0.01 μgm−3 and MAE 0.09 μgm−3) and RF (RMSE 1.27 μgm−3 and MAE 0.86 μgm−3). For PM10.0, SVR-L leads to best results (both RMSE and MAE 0.06 μgm−3), followed by FFNN (RMSE 0.13 μgm−3 and MAE 0.09 μgm−3) and RF (RMSE 1.60 μgm−3 and MAE 1.16 μgm−3). For PM2.5/PM10.0, FFNN is the best and accurate method for prediction (0.001 for both RMSE and MAE), followed by RF (0.02 for both RMSE and MAE) and SVR-L (RMSE 0.05 μgm−3 and MAE 0.04).

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