A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence

2014 ◽  
Vol 62 ◽  
pp. 139-152 ◽  
Author(s):  
Andreas Efstratiadis ◽  
Yannis G. Dialynas ◽  
Stefanos Kozanis ◽  
Demetris Koutsoyiannis
Keyword(s):  
Time Series ◽  
Stochastic Model ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Synthetic Time Series

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 Spatial and Temporal Analyses of Vegetation Changes at Multiple Time Scales in the Qilian Mountains

2021 ◽  
Vol 13 (24) ◽  
pp. 5046
Author(s):  
Lifeng Zhang ◽  
Haowen Yan ◽  
Lisha Qiu ◽  
Shengpeng Cao ◽  
Yi He ◽  
...  
Keyword(s):  
Time Scales ◽  
Qilian Mountains ◽  
Dominant Factor ◽  
Multiple Time Scales ◽  
Vegetation Changes ◽  
Multiple Time ◽  
Temperature And Precipitation ◽  
The Qilian Mountains ◽  
Vegetation Variation

The Qilian Mountains (QLMs), an important ecological protective barrier and major water resource connotation area in the Hexi Corridor region, have an important impact on ecological security in western China due to their ecological changes. However, most existing studies have investigated vegetation changes and their main driving forces in the QLMs on the basis of a single scale. Thus, the interactions among multiple environmental factors in the QLMs are still unclear. This study was based on normalised difference vegetation index (NDVI) data from 2000 to 2019. We systematically analysed the spatial and temporal characteristics of the QLMs at multiple time scales using trend analysis, ensemble empirical mode decomposition, Geodetector, and correlation analysis methods. At different time scales under single-factor and multi-factor interactions, we examined the mechanisms of the vegetation changes and their drivers. Our results showed that the vegetation in the QLMs showed a trend of overall improvement in 2000–2019, at a rate of 0.88 × 10−3, mainly in the central western regions. The NDVI in the QLMs showed a short change cycle of 3 and 5 years and a long-term trend. Sunshine time and wind speed were the main drivers of the vegetation variation in the QLMs, followed by temperature. Precipitation affected the vegetation spatial variation within a certain altitude range. However, temperature and precipitation had stronger explanatory powers for the vegetation variation in the western QLMs than in the eastern part. Their interaction was the dominant factor in the regional differences in vegetation. The responses of the NDVI to temperature and precipitation were stronger in the long time series. The main drivers of vegetation variation were land surface temperature and precipitation in the east and temperature and evapotranspiration in the west. Precipitation was the main driver of vegetation growth in the northern and southwestern QLMs on both the short- and long-term scales. Vegetation changes were more significantly influenced by short-term temperature changes in the east but by a combination of temperature and precipitation in most parts of the QLMs on a 5-year time scale.

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.

SEVERAL FUNDAMENTAL PROPERTIES OF DCCA CROSS-CORRELATION COEFFICIENT

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750017 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
JINGJING HUANG
Keyword(s):  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Stationary Time Series ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Linear Measure ◽  
Fundamental Properties ◽  
Cross Correlation Analysis ◽  
Synthetic Time Series

The (detrended cross-correlation analysis) DCCA cross-correlation coefficient was proposed to measure the level of long-range cross-correlations between two non-stationary time series on multiple time scales. It has been applied to diverse areas of interest, although many properties of this method are not clear. In this paper, we theoretically study several fundamental properties of the DCCA cross-correlation coefficient, which contributes to acquiring more statistical characteristics of this measure. We resort to a synthetic time series that is followed by the integration and the detrending procedures of the DCCA cross-correlation coefficient, which divide the steps to estimate the coefficient into two portions. The former portion, including the integration and the detrending, is proved to be a linear transformation. The second portion is devoted to measuring Pearson’s [Formula: see text] between two synthetic time series. We confirm that the DCCA cross-correlation coefficient is also a linear measure by definition. The simulations including the ARFIMA processes and the multifractal binomial measures are numerically analyzed, which confirm the theoretical analysis.

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.

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.

Multiscale analysis of long-term recordings from unanesthetized rats unveils multiple time scales inherent in the neural dynamics

2010 ◽  
Vol 68 ◽  
pp. e122
Author(s):  
Hideyuki Cateau ◽  
Leonid Safonov ◽  
Yoshikazu Isomura ◽  
Siu Kang ◽  
Zbigniew Struzik ◽  
...  
Keyword(s):  
Time Scales ◽  
Multiscale Analysis ◽  
Neural Dynamics ◽  
Multiple Time Scales ◽  
Multiple Time
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