EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

The Dynamics of a Flexible Levitated Droplet

2001 ◽  
Author(s):  
Mihai Dupac ◽  
Dan B. Marghitu ◽  
David G. Beale
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Data ◽  
Simulated Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Dynamics Analysis ◽  
Attractor Dimension ◽  
Levitated Droplet

Abstract In this paper, a nonlinear dynamics analysis of the simulated data was considered to study the time evolution of an electro-magnetically levitated flexible droplet. The main goals of this work are to study the behavior of the levitated droplet and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed.

scholarly journals Evaluation of Test Statistics for Detection of Outliers and Shifts

2020 ◽  
Vol 4 (2) ◽  
pp. 54-75
Author(s):  
Amena Urooj ◽  
Zahid Asghar
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Structural Breaks ◽  
Time Series Data ◽  
Model Identification ◽  
Small Sample ◽  
Critical Values ◽  
Series Data ◽  
Test Statistics ◽  
The Impact

Existence of outliers and structural breaks having mutually unknown nature, in time series data, offer challenges to data analysts in model identification, estimation and validation. Detection of these outliers has been an important area of research in time series since long. To analyze the impact of these structural breaks and outliers on model identification, estimation and their inferential analysis, we use two data generating processes: MA(1) and ARMA(1,1). The performance of the test statistics for detecting additive outlier(AO), innovative outlier(IO), level shift(LS) and transient change(TC) is investigated using simulation strategy through power of a test, empirical level of significance, empirical critical values, misspecification frequencies and sampling distribution of estimators for the two models. The empirical critical values are found higher than the theoretical cut-off points, empirical power of the test statistics is not satisfactory for small sample size, large cut-off points and large model coefficient. We have explored confusion between LS, AO, TC and IO at different critical values(c) by varying sample size. We have also collected empirical evidence from time series data for Pakistan using 3-stage iterative procedure to detect multiple outliers and structural breaks. We find that neglecting shocks lead to wrong identification, biased estimation and excess kurtosis. JEL Classification Codes: C15, C18, C63, C32, C87, C51, C52, C82 AMS Classification Codes: 62, 65, 91, DI, 62-08, 62J20, 00A72, 91-08, 91-10, 91-11 62P20, 91B82, 91B84, 62M07, 62M09, 62M10, 62M15, 62M20

scholarly journals A Comparison of Time-Series Predictions for Healthcare Emergency Department Indicators and the Impact of COVID-19

2021 ◽  
Vol 11 (8) ◽  
pp. 3561
Author(s):  
Diego Duarte ◽  
Chris Walshaw ◽  
Nadarajah Ramesh
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
General Regression Neural Network ◽  
Series Data ◽  
Machine Learning Model ◽  
Hospital Patients ◽  
Major Incidents ◽  
General Regression ◽  
The Impact

Across the world, healthcare systems are under stress and this has been hugely exacerbated by the COVID pandemic. Key Performance Indicators (KPIs), usually in the form of time-series data, are used to help manage that stress. Making reliable predictions of these indicators, particularly for emergency departments (ED), can facilitate acute unit planning, enhance quality of care and optimise resources. This motivates models that can forecast relevant KPIs and this paper addresses that need by comparing the Autoregressive Integrated Moving Average (ARIMA) method, a purely statistical model, to Prophet, a decomposable forecasting model based on trend, seasonality and holidays variables, and to the General Regression Neural Network (GRNN), a machine learning model. The dataset analysed is formed of four hourly valued indicators from a UK hospital: Patients in Department; Number of Attendances; Unallocated Patients with a DTA (Decision to Admit); Medically Fit for Discharge. Typically, the data exhibit regular patterns and seasonal trends and can be impacted by external factors such as the weather or major incidents. The COVID pandemic is an extreme instance of the latter and the behaviour of sample data changed dramatically. The capacity to quickly adapt to these changes is crucial and is a factor that shows better results for GRNN in both accuracy and reliability.

scholarly journals Assessing Stream-Aquifer Connectivity in a Coastal California Watershed

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 416
Author(s):  
Bwalya Malama ◽  
Devin Pritchard-Peterson ◽  
John J. Jasbinsek ◽  
Christopher Surfleet
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Water Level ◽  
Time Series Data ◽  
Series Data ◽  
Low Permeability ◽  
Pumping Tests ◽  
Stream Flows ◽  
The Impact

We report the results of field and laboratory investigations of stream-aquifer interactions in a watershed along the California coast to assess the impact of groundwater pumping for irrigation on stream flows. The methods used include subsurface sediment sampling using direct-push drilling, laboratory permeability and particle size analyses of sediment, piezometer installation and instrumentation, stream discharge and stage monitoring, pumping tests for aquifer characterization, resistivity surveys, and long-term passive monitoring of stream stage and groundwater levels. Spectral analysis of long-term water level data was used to assess correlation between stream and groundwater level time series data. The investigations revealed the presence of a thin low permeability silt-clay aquitard unit between the main aquifer and the stream. This suggested a three layer conceptual model of the subsurface comprising unconfined and confined aquifers separated by an aquitard layer. This was broadly confirmed by resistivity surveys and pumping tests, the latter of which indicated the occurrence of leakage across the aquitard. The aquitard was determined to be 2–3 orders of magnitude less permeable than the aquifer, which is indicative of weak stream-aquifer connectivity and was confirmed by spectral analysis of stream-aquifer water level time series. The results illustrate the importance of site-specific investigations and suggest that even in systems where the stream is not in direct hydraulic contact with the producing aquifer, long-term stream depletion can occur due to leakage across low permeability units. This has implications for management of stream flows, groundwater abstraction, and water resources management during prolonged periods of drought.

Welfare Use in Japan: Trends and Determinants

2007 ◽  
pp. 88
Author(s):  
Wataru Suzuki ◽  
Yanfei Zhou
Keyword(s):  
Time Series ◽  
Longitudinal Data ◽  
Time Series Data ◽  
Positive Impact ◽  
Series Data ◽  
Negative Effects ◽  
Long Time ◽  
Welfare Use ◽  
The Impact

This article represents the first step in filling a large gap in knowledge concerning why Public Assistance (PA) use recently rose so fast in Japan. Specifically, we try to address this problem not only by performing a Blanchard and Quah decomposition on long-term monthly time series data (1960:04-2006:10), but also by estimating prefecturelevel longitudinal data. Two interesting findings emerge from the time series analysis. The first is that permanent shock imposes a continuously positive impact on the PA rate and is the main driving factor behind the recent increase in welfare use. The second finding is that the impact of temporary shock will last for a long time. The rate of the use of welfare is quite rigid because even if the PA rate rises due to temporary shocks, it takes about 8 or 9 years for it to regain its normal level. On the other hand, estimations of prefecture-level longitudinal data indicate that the Financial Capability Index (FCI) of the local government2 and minimum wage both impose negative effects on the PA rate. We also find that the rapid aging of Japan's population presents a permanent shock in practice, which makes it the most prominent contribution to surging welfare use.

scholarly journals Political Stability and its Impact on Economic Growth of Pakistan (1988-2018): A Time Series Analysis

2020 ◽  
Vol 6 (1) ◽  
pp. 273-282
Author(s):  
Majid Hussain Phul ◽  
Muhammad Saleem Rahpoto ◽  
Ghulam Muhammad Mangnejo
Keyword(s):  
Economic Growth ◽  
Time Series ◽  
Time Series Data ◽  
Political Stability ◽  
Series Data ◽  
Explanatory Variables ◽  
Long Run ◽  
Short Run ◽  
The Impact ◽  
Positive Effect

This research paper empirically investigates the outcome of Political stability on economic growth (EG) of Pakistan for the period of 1988 to 2018. Political stability (PS), gross fixed capital formation (GFCF), total labor force (TLF) and Inflation (INF) are important explanatory variables. Whereas for model selection GDPr is used as the dependent variable. To check the stationary of time series data Augmented Dickey Fuller (ADF) unit root (UR) test has been used,  and whereas to find out the long run relationship among variables, OLS method has been used. The analysis the impact of PS on EG (EG) in the short run, VAR model has been used. The outcomes show that all the variables (PS, GFCF, TLF and INF) have a significantly positive effect on the EG of Pakistan in the long run period. But the effect of PS on GDP is smaller. Further, in this research we are trying to see the short run relationship between GDP and other explanatory variables. The outcomes show that PS does not have such effect on GDP in the short run analysis. While GFCF, TLF and INF have significantly positive effect on GDP of Pakistan in the short run period.

scholarly journals The Effect of IJ-EPA to Indonesia Export: Interupted Time Series (ITS) Approach

2020 ◽  
Vol 2 (1) ◽  
pp. 128-145
Author(s):  
Yuafanda Kholfi Hartono ◽  
Sumarto Eka Putra
Keyword(s):  
Time Series ◽  
Free Trade ◽  
Free Trade Agreement ◽  
Time Series Data ◽  
Current Account Deficit ◽  
Trade Agreement ◽  
Export Market ◽  
Series Data ◽  
The Government ◽  
The Impact

Indonesia Japan Economic Partnership Agreement (IJ-EPA) is a bilateral free-trade agreement between Indonesia and Japan that has been started from July 1st, 2008. After more than a decade of its implementation, there is a question that we need to be addressed: Does liberalization of IJ-EPA make Indonesia’s export to Japan increase? This question is important since the government gives a trade-off by giving lower tariff for certain commodities agreed in agreement to increase export. Using Interrupted time series (ITS) analysis based on time-series data from Statistics Indonesia (BPS), this article found that the impact of IJ-EPA decreased for Indonesia export to Japan. Furthermore, this paper proposed some potential commodities that can increase the effectiveness of this FTA. The importance of this topic is that Indonesia will maximize the benefit in implementing of agreement that they made from the third biggest destination export of their total export value, so it will be in line with the government's goal to expand export market to solve current account deficit. In addition, the method that used in this paper can be implemented to other countries so that they can maximize the effect of Free Trade Agreement, especially for their export.

scholarly journals Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 25-46 ◽  
Author(s):  
Merten Stender ◽  
Sebastian Oberst ◽  
Norbert Hoffmann
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Time Series Data ◽  
Model Identification ◽  
Transient Behavior ◽  
Series Data ◽  
Special Focus ◽  
Suitable Model ◽  
Reconstruction Method ◽  
Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

scholarly journals Uncertainty Analysis of Object-Based Land-Cover Classification Using Sentinel-2 Time-Series Data

2020 ◽  
Vol 12 (22) ◽  
pp. 3798
Author(s):  
Lei Ma ◽  
Michael Schmitt ◽  
Xiaoxiang Zhu
Keyword(s):  
Time Series ◽  
Land Cover ◽  
Time Series Data ◽  
Land Cover Classification ◽  
Series Data ◽  
Spectral Bands ◽  
Object Based ◽  
Spatio Temporal ◽  
Optical Satellite Images ◽  
The Impact

Recently, time-series from optical satellite data have been frequently used in object-based land-cover classification. This poses a significant challenge to object-based image analysis (OBIA) owing to the presence of complex spatio-temporal information in the time-series data. This study evaluates object-based land-cover classification in the northern suburbs of Munich using time-series from optical Sentinel data. Using a random forest classifier as the backbone, experiments were designed to analyze the impact of the segmentation scale, features (including spectral and temporal features), categories, frequency, and acquisition timing of optical satellite images. Based on our analyses, the following findings are reported: (1) Optical Sentinel images acquired over four seasons can make a significant contribution to the classification of agricultural areas, even though this contribution varies between spectral bands for the same period. (2) The use of time-series data alleviates the issue of identifying the “optimal” segmentation scale. The finding of this study can provide a more comprehensive understanding of the effects of classification uncertainty on object-based dense multi-temporal image classification.

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