scholarly journals Multivariate and multi-scale generator based on non-parametric stochastic algorithms

2019 ◽  
Vol 21 (6) ◽  
pp. 1102-1117
Author(s):  
Đurica Marković ◽  
Siniša Ilić ◽  
Dragutin Pavlović ◽  
Jasna Plavšić ◽  
Nesa Ilich
Keyword(s):  
Time Series ◽  
Case Studies ◽  
Time Scales ◽  
Multivariate Time Series ◽  
Simulated Data ◽  
Frequency Distributions ◽  
Skewness Coefficient ◽  
Streamflow Statistics ◽  
Relative Errors ◽  
Non Parametric

Abstract A method for generating combined multivariate time series at multiple locations and at different time scales is presented. The procedure is based on three steps: first, the Monte Carlo method generation of data with statistical properties as close as possible to the observed series; second, the rearrangement of the order of simulated data in the series to achieve target correlations; and third, the permutation of series for correlation adjustment between consecutive years. The method is non-parametric and retains, to a satisfactory degree, the properties of the observed time series at the selected simulation time scale and at coarser time scales. The new approach is tested on two case studies, where it is applied to the log-transformed streamflow and precipitation at weekly and monthly time scales. Special attention is given to the extrapolation of non-parametric cumulative frequency distributions in their tail zones. The results show a good agreement of stochastic properties between the simulated and observed data. For example, for one of the case studies, the average relative errors of the observed and simulated weekly precipitation and streamflow statistics (up to skewness coefficient) are in the range of 0.1–9.2% and 0–5.4%, respectively.

scholarly journals Analysis Methods for Characterizing Salinity Variability from Multivariate Time Series Applied to the Apalachicola Bay Estuary

2012 ◽  
Vol 29 (4) ◽  
pp. 613-628 ◽  
Author(s):  
Steven L. Morey ◽  
Dmitry S. Dukhovskoy
Keyword(s):  
Time Series ◽  
Time Scales ◽  
River Discharge ◽  
River Flow ◽  
High Salinity ◽  
Multivariate Time Series ◽  
Salinity Range ◽  
Apalachicola Bay ◽  
Analysis Methods ◽  
Salinity Variability

Abstract Statistical analysis methods are developed to quantify the impacts of multiple forcing variables on the hydrographic variability within an estuary instrumented with an enduring observational system. The methods are applied to characterize the salinity variability within Apalachicola Bay, a shallow multiple-inlet estuary along the northeastern Gulf of Mexico coast. The 13-yr multivariate time series collected by the National Estuary Research Reserve at three locations within the bay are analyzed to determine how the estuary responds to variations in external forcing mechanisms, such as freshwater discharge, precipitation, tides, and local winds at multiple time scales. The analysis methods are used to characterize the estuarine variability under differing flow regimes of the Apalachicola River, a managed waterway, with particular focus on extreme events and scales of variability that are critical to local ecosystems. Multivariate statistical models are applied that describe the salinity response to winds from multiple directions, river flow, and precipitation at daily, weekly, and monthly time scales to understand the response of the estuary under different climate regimes. Results show that the salinity is particularly sensitive to river discharge and wind magnitude and direction, with local precipitation being largely unimportant. Applying statistical analyses with conditional sampling quantifies how the likelihoods of high-salinity and long-duration high-salinity events, conditions of critical importance to estuarine organisms, change given the state of the river flow. Intraday salinity range is shown to be negatively correlated with the salinity, and correlated with river discharge rate.

scholarly journals Unsupervised Pre-training of a Deep LSTM-based Stacked Autoencoder for Multivariate Time Series Forecasting Problems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Alaa Sagheer ◽  
Mostafa Kotb
Keyword(s):  
Time Series ◽  
Case Studies ◽  
Real World ◽  
Time Series Data ◽  
Short Term Memory ◽  
Multivariate Time Series ◽  
Series Data ◽  
Recurrent Networks ◽  
Stacked Autoencoder ◽  
Real World Datasets

AbstractCurrently, most real-world time series datasets are multivariate and are rich in dynamical information of the underlying system. Such datasets are attracting much attention; therefore, the need for accurate modelling of such high-dimensional datasets is increasing. Recently, the deep architecture of the recurrent neural network (RNN) and its variant long short-term memory (LSTM) have been proven to be more accurate than traditional statistical methods in modelling time series data. Despite the reported advantages of the deep LSTM model, its performance in modelling multivariate time series (MTS) data has not been satisfactory, particularly when attempting to process highly non-linear and long-interval MTS datasets. The reason is that the supervised learning approach initializes the neurons randomly in such recurrent networks, disabling the neurons that ultimately must properly learn the latent features of the correlated variables included in the MTS dataset. In this paper, we propose a pre-trained LSTM-based stacked autoencoder (LSTM-SAE) approach in an unsupervised learning fashion to replace the random weight initialization strategy adopted in deep LSTM recurrent networks. For evaluation purposes, two different case studies that include real-world datasets are investigated, where the performance of the proposed approach compares favourably with the deep LSTM approach. In addition, the proposed approach outperforms several reference models investigating the same case studies. Overall, the experimental results clearly show that the unsupervised pre-training approach improves the performance of deep LSTM and leads to better and faster convergence than other models.

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.

Non-parametric Multivariate Time Series Co-clustering Model Applied to Driving-Assistance Systems Validation

2021 ◽  
pp. 71-87
Author(s):  
Etienne Goffinet ◽  
Mustapha Lebbah ◽  
Hanane Azzag ◽  
Giraldi Loïc ◽  
Anthony Coutant
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Clustering Model ◽  
Driving Assistance ◽  
Assistance Systems ◽  
Non Parametric

scholarly journals Detecting correlation changes in multivariate time series: A comparison of four non-parametric change point detection methods

2016 ◽  
Vol 49 (3) ◽  
pp. 988-1005 ◽  
Author(s):  
Jedelyn Cabrieto ◽  
Francis Tuerlinckx ◽  
Peter Kuppens ◽  
Mariel Grassmann ◽  
Eva Ceulemans
Keyword(s):  
Time Series ◽  
Change Point ◽  
Multivariate Time Series ◽  
Change Point Detection ◽  
Detection Methods ◽  
Parametric Change ◽  
Point Detection ◽  
Non Parametric

scholarly journals Outlier Detection for Multivariate Time Series Using Dynamic Bayesian Networks

2021 ◽  
Vol 11 (4) ◽  
pp. 1955
Author(s):  
Jorge L. Serras ◽  
Susana Vinga ◽  
Alexandra M. Carvalho
Keyword(s):  
Time Series ◽  
Outlier Detection ◽  
Web Application ◽  
Detection System ◽  
Multivariate Time Series ◽  
Dynamic Bayesian Network ◽  
Simulated Data ◽  
Real Data ◽  
Dynamic Bayesian Networks ◽  
Detection Methods

Outliers are observations suspected of not having been generated by the underlying process of the remaining data. Many applications require a way of identifying interesting or unusual patterns in multivariate time series (MTS), now ubiquitous in many applications; however, most outlier detection methods focus solely on univariate series. We propose a complete and automatic outlier detection system covering the pre-processing of MTS data that adopts a dynamic Bayesian network (DBN) modeling algorithm. The latter encodes optimal inter and intra-time slice connectivity of transition networks capable of capturing conditional dependencies in MTS datasets. A sliding window mechanism is employed to score each MTS transition gradually, given the DBN model. Two score-analysis strategies are studied to assure an automatic classification of anomalous data. The proposed approach is first validated in simulated data, demonstrating the performance of the system. Further experiments are made on real data, by uncovering anomalies in distinct scenarios such as electrocardiogram series, mortality rate data, and written pen digits. The developed system proved beneficial in capturing unusual data resulting from temporal contexts, being suitable for any MTS scenario. A widely accessible web application employing the complete system is publicly available jointly with a tutorial.

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