scholarly journals Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 385 ◽  
Author(s):  
David Cuesta-Frau ◽  
Juan Pablo Murillo-Escobar ◽  
Diana Alexandra Orrego ◽  
Edilson Delgado-Trejos
Keyword(s):  
Time Series ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Series Length ◽  
Stability Point ◽  
Long Time ◽  
Model Time Series ◽  
The Stability ◽  
Forbidden Patterns ◽  
Short Time

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Analysing “Long Data” on Collective Violence in Indonesia

2015 ◽  
Vol 43 (5) ◽  
pp. 613-633
Author(s):  
David A. Meyer ◽  
Arthur Stein
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Model Building ◽  
Collective Violence ◽  
Temporal Data ◽  
Data Set ◽  
Time Correlations ◽  
Long Time ◽  
Short Time ◽  
Periodic Components

“Long data”, i.e., temporal data disaggregated to short time intervals to form a long time series, is a particularly interesting type of “big data”. Financial data are often available in this form (e.g., many years of daily stock prices), but until recently long data for other social, and even other economic, processes have been rare. Over the last decade, however, long data have begun to be extracted from (digitized) text, and then used to assess or formulate micro-level and macro-level theories. The UN Support Facility for Indonesian Recovery (UNSFIR) collected a long data set of incidents of collective violence in 14 Indonesian provinces during the 14 year period 1990–2003. In this paper we exploit the “length” of the UNSFIR data by applying several time series analysis methods. These reveal some previously unobserved features of collective violence in Indonesia—including periodic components and long time correlations—with important social/political interpretations and consequences for explanatory model building.

scholarly journals Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants

2021 ◽  
Author(s):  
Airton Monte Serrat Borin ◽  
Anne Humeau-Heurtier ◽  
Luiz Otavio Murta ◽  
Luiz Eduardo Virgilio Silva
Keyword(s):  
Time Series ◽  
Multiscale Entropy ◽  
Entropy Analysis ◽  
Short Term ◽  
Series Length ◽  
Short Time Series ◽  
Fuzzy Algorithms ◽  
Computing Performance ◽  
Similar Accuracy ◽  
Short Time

Abstract Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

scholarly journals Embedding reconstruction methodology for short time series – application to large El Niño events

2010 ◽  
Vol 17 (6) ◽  
pp. 753-764 ◽  
Author(s):  
H. F. Astudillo ◽  
F. A. Borotto ◽  
R. Abarca-del-Rio
Keyword(s):  
Time Series ◽  
El Niño ◽  
Time Delays ◽  
El Nino ◽  
Southern Oscillation ◽  
Dimensional Subspace ◽  
Reconstruction Method ◽  
Short Time Series ◽  
Long Time ◽  
Short Time

Abstract. We propose an alternative approach for the embedding space reconstruction method for short time series. An m-dimensional embedding space is reconstructed with a set of time delays including the relevant time scales characterizing the dynamical properties of the system. By using a maximal predictability criterion a d-dimensional subspace is selected with its associated set of time delays, in which a local nonlinear blind forecasting prediction performs the best reconstruction of a particular event of a time series. An locally unfolded d-dimensional embedding space is then obtained. The efficiency of the methodology, which is mathematically consistent with the fundamental definitions of the local nonlinear long time-scale predictability, was tested with a chaotic time series of the Lorenz system. When applied to the Southern Oscillation Index (SOI) (observational data associated with the El Niño-Southern Oscillation phenomena (ENSO)) an optimal set of embedding parameters exists, that allows constructing the main characteristics of the El Niño 1982–1983 and 1997–1998 events, directly from measurements up to 3 to 4 years in advance.

scholarly journals Predicting the Health Condition of mHealth App Users with Large Differences in the Number of Recorded Observations - Where to Learn from?

2020 ◽  
pp. 659-673
Author(s):  
Vishnu Unnikrishnan ◽  
Yash Shah ◽  
Miro Schleicher ◽  
Mirela Strandzheva ◽  
Plamen Dimitrov ◽  
...  
Keyword(s):  
Time Series ◽  
Pilot Study ◽  
Predictive Model ◽  
Health Condition ◽  
Diabetic Patients ◽  
User Engagement ◽  
Series Length ◽  
Short Time ◽  
Mhealth Apps ◽  
Over Time

Abstract Some mHealth apps record user activity continuously and unobtrusively, while other apps rely by nature on user engagement and self-discipline: users are asked to enter data that cannot be assessed otherwise, e.g., on how they feel and what non-measurable symptoms they have. Over time, this leads to substantial differences in the length of the time series of recordings for the different users. In this study, we propose two algorithms for wellbeing-prediction from such time series, and we compare their performance on the users of a pilot study on diabetic patients - with time series length varying between 8 and 87 recordings. Our first approach learns a model from the few users, on which many recordings are available, and applies this model to predict the 2nd, 3rd, and so forth recording of users newly joining the mHealth platform. Our second approach rather exploits the similarity among the first few recordings of newly arriving users. Our results for the first approach indicate that the target variable for users who use the app for long are not predictive for users who use the app only for a short time. Our results for the second approach indicate that few initial recordings suffice to inform the predictive model and improve performance considerably.

scholarly journals MEMBANGUN MODEL PENYEBARAN PENYAKIT AKIBAT ASAP KEBAKARAN HUTAN

2018 ◽  
Vol 15 (1) ◽  
pp. 36-47
Author(s):  
B Kurniawan ◽  
R Ratianingsih ◽  
Hajar Hajar
Keyword(s):  
Critical Points ◽  
Forest Fires ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Short Time Period ◽  
Time Period ◽  
Long Time ◽  
The Stability ◽  
Short Time ◽  
Threshold Point

Forest fires impact a very serious problem because it could cause health problem, especially respiratory disease such as (ISPA), Asthma and Bronchitis. The study of the health disorders is conducted by consider mathematicaly the spread of disease due to forest fires smoke. The model is constructed by devide the human population into six subpopulations, that is vulnerable S(t), exposed E(t), Asthma infected A(t), Bronchitis infected B(t) and recovered R(t).The governed model is analyted at every critical points using Routh-Hurwitz method. The results gives two critical points that describe a free disease conditions ( ) and an endemic conditions ( ). A stabil ( ) is occured if  and  where the threshold point of the stability is expressed as  and   . Endemic conditions  will be asymptotically stable when  and  with  . The condition of free disease of forest fires is occured in a long time period, while the endemic conditions is occurred in a short time period. It could be interpreted that the disease spread due to the forest fires smoke is not easy to overcome.

scholarly journals Detection of Dynamical Regime Transitions with Lacunarity as a Multiscale Recurrence Quantification Measure

2020 ◽  
Author(s):  
Tobias Braun ◽  
Norbert Marwan ◽  
Vishnu R. Unni ◽  
Raman I. Sujith ◽  
Juergen Kurths
Keyword(s):  
Time Series ◽  
Recurrence Plot ◽  
Dynamical Regime ◽  
Series Length ◽  
Dynamical Complexity ◽  
Recurrence Quantification ◽  
The Rich ◽  
Short Time ◽  
Recurrent Patterns ◽  
Regime Transitions

<p>We propose Lacunarity as a novel recurrence quantification measure and apply it in the context of dynamical regime transitions. Many complex real-world systems exhibit abrupt regime shifts. We carry out a recurrence plot based analysis for different paradigmatic systems and thermoacoustic combustion time series in order to demonstrate the ability of our method to detect dynamical transitions on variable temporal scales. Lacunarity is usually interpreted as a measure of ‘gappiness’ of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogenity in the temporal recurrent patterns. Our method succeeds to distinguish states of varying dynamical complexity in presence of noise and short time series length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and features beyond the scope of line structures can be accounted for. Applied to acoustic pressure fluctuation time series, it captures both the rich variability in dynamical complexity and detects shifts of characteristic time scales.</p>

Return calculation methodology: Evidence from the Hungarian mutual fund industry

2009 ◽  
Vol 59 (4) ◽  
pp. 391-409 ◽  
Author(s):  
P. Erdős ◽  
M. Ormos
Keyword(s):  
Time Series ◽  
Mutual Fund ◽  
Market Model ◽  
Monthly Return ◽  
Calculation Methodology ◽  
Long Time ◽  
Asymptotic Tests ◽  
Best Fitting ◽  
One Year ◽  
Short Time

In the empirical finance literature most frequently monthly returns are applied for measuring fund performance or testing market efficiency. We propose a new return calculation method, the daily recalculated monthly returns which has not been used in academic studies for asset pricing purposes. We argue that our method outperforms daily and monthly return calculations in the case of Hungarian mutual funds when only short time series are available. Daily recalculated monthly returns induce the best fitting property of the market model while the time series remain sufficiently long to derive asymptotic tests even when we work on a one-year-long time series. Using our method the estimated parameters and the R2 s are very close to the results obtained when using monthly returns which are considered a good working approximation.

scholarly journals Continuous microwave pasteurization of a vegetable smoothie improves its physical quality and hinders detrimental enzyme activity

2016 ◽  
Vol 23 (1) ◽  
pp. 36-45 ◽  
Author(s):  
Mitra Arjmandi ◽  
Mariano Otón ◽  
Francisco Artés ◽  
Francisco Artés-Hernández ◽  
Perla A Gómez ◽  
...  
Keyword(s):  
Microwave Heating ◽  
High Power ◽  
Pectin Methylesterase ◽  
Color Retention ◽  
Higher Power ◽  
Long Time ◽  
Hue Angle ◽  
Microwave Pasteurization ◽  
The Stability ◽  
Short Time

The effect of a pasteurization treatment at 90 ± 2 ℃ for 35 s provided by continuous microwave under different doses (low power/long time and high power/short time) or conventional pasteurization on the quality of orange-colored smoothies and their changes throughout 45 days of storage at 5 ℃ was investigated. A better color retention of the microwave pasteurization- treated smoothie using high power/short time than in conventionally processed sample was evidenced by the stability of the hue angle. The continuous microwave heating increased the viscosity of the smoothie more than the conventional pasteurization in comparison with non-treated samples. Lower residual enzyme activities from peroxidase, pectin methylesterase and polygalacturonase were obtained under microwave heating, specifically due to the use of higher power/shorter time. For this kind of smoothie, polygalacturonase was the more thermo-resistant enzyme and could be used as an indicator of pasteurization efficiency. The use of a continuous semi-industrial microwave using higher power and shorter time, such as 1600 W/206 s and 3600 W/93 s, resulted in better quality smoothies and greater enzyme reduction than conventional thermal treatment.

scholarly journals Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 913 ◽  
Author(s):  
Hamed Azami ◽  
Alberto Fernández ◽  
Javier Escudero
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Channel Noise ◽  
Original Algorithm ◽  
Times Series ◽  
Non Linear ◽  
Long Time ◽  
Spatial Domains ◽  
The Stability ◽  
Multivariate Signals

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

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