Estimation of the coupling delay time from time series of self-oscillatory systems with allowance for the autocorrelation function of phase noise

2014 ◽  
Vol 40 (10) ◽  
pp. 934-936 ◽  
Author(s):  
E. V. Sidak ◽  
D. A. Smirnov ◽  
B. P. Bezruchko
Keyword(s):  
Time Series ◽  
Phase Noise ◽  
Autocorrelation Function ◽  
Delay Time ◽  
Coupling Delay ◽  
Oscillatory Systems ◽  
Coupling Delay Time

PARAMETER MISMATCHES AND INVERSE SYNCHRONIZATION IN THE IKEDA MODEL

2004 ◽  
Vol 18 (13) ◽  
pp. 1911-1918 ◽  
Author(s):  
E. M. SHAHVERDIEV ◽  
R. A. NURIEV ◽  
R. H. HASHIMOV
Keyword(s):  
Numerical Simulations ◽  
Delay Time ◽  
Analytical Approach ◽  
Coupled Systems ◽  
Stability Conditions ◽  
Crucial Importance ◽  
Parameter Mismatch ◽  
Coupling Delay ◽  
Existence And Stability ◽  
Coupling Delay Time

We investigate inverse retarded synchronization between two uni-directionally linearly coupled chaotic non-identical Ikeda models and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only inverse retarded synchronization with the coupling delay time is obtained. We derive existence and stability conditions for the inverse retarded synchronization manifold. We show that with parameter mismatch or without it neither inverse complete nor inverse anticipating synchronization occurs. Numerical simulations fully support the analytical approach.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

scholarly journals SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 602
Author(s):  
Luisa Martínez-Acosta ◽  
Juan Pablo Medrano-Barboza ◽  
Álvaro López-Ramos ◽  
John Freddy Remolina López ◽  
Álvaro Alberto López-Lambraño
Keyword(s):  
Time Series ◽  
Water Resources ◽  
Autocorrelation Function ◽  
Information Criterion ◽  
Monthly Rainfall ◽  
Statistical Characteristics ◽  
Rainfall Time Series ◽  
River Watershed ◽  
Statistical Measures ◽  
Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

scholarly journals Estimation of Delay Times in Coupling Between Autonomic Regulatory Loops of Human Heart Rate and Blood Flow Using Phase Dynamics Analysis

2017 ◽  
Vol 9 (1) ◽  
pp. 16-22 ◽  
Author(s):  
Vladimir S Khorev ◽  
Anatoly S Karavaev ◽  
Elena E Lapsheva ◽  
Tatyana A Galushko ◽  
Mikhail D Prokhorov ◽  
...  
Keyword(s):  
Heart Rate ◽  
Delay Time ◽  
Healthy Subjects ◽  
Low Frequency ◽  
Phase Dynamics ◽  
Oscillatory Systems ◽  
Low Frequency Oscillations ◽  
Delay Times ◽  
The Difference ◽  
Regulatory Loop

Objective: We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations. Material and Methods: In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops. Results: Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds. Conclusion: Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

Predicting Daily Confirmed COVID-19 Cases in India

2021 ◽  
pp. 34-51
Author(s):  
Sudip Singh
Keyword(s):  
Time Series ◽  
Root Mean Square Error ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Arima Model ◽  
Family Welfare ◽  
Mean Square ◽  
Univariate Time Series ◽  
Partial Autocorrelation Function ◽  
Auto Regressive

India, with a population of over 1.38 billion, is facing high number of daily COVID-19 confirmed cases. In this chapter, the authors have applied ARIMA model (auto-regressive integrated moving average) to predict daily confirmed COVID-19 cases in India. Detailed univariate time series analysis was conducted on daily confirmed data from 19.03.2020 to 28.07.2020, and the predictions from the model were satisfactory with root mean square error (RSME) of 7,103. Data for this study was obtained from various reliable sources, including the Ministry of Health and Family Welfare (MoHFW) and http://covid19india.org/. The model identified was ARIMA(1,1,1) based on time series decomposition, autocorrelation function (ACF), and partial autocorrelation function (PACF).

scholarly journals Characteristics of extreme heavy precipitation events occurring in the area of Cracow (Poland)

2014 ◽  
Vol 9 (No. 4) ◽  
pp. 182-191 ◽  
Author(s):  
A. Walega ◽  
B. Michalec
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Heavy Precipitation ◽  
Botanical Garden ◽  
Maximum Precipitation ◽  
Density Analysis ◽  
Increasing Precipitation ◽  
Precipitation Events

The variability of extremely heavy precipitation events with duration of 120 min occurring in the area of Cracow, southern Poland was assessed. The analysis was performed using time series of maximum annual precipitation events with durations t = 5, 10, 15, 30, 60, and 120 min, recorded at the Botanical Garden station at the Jagiellonian University in the period of 1906–1990. The periodicity of precipitation was analyzed using the autocorrelation function and Fourier spectral density analysis. The Probable Maximum Precipitation (PMP) was calculated by Hershfield’s statistical method. The analysis of the autocorrelation function of sequences and the Fourier spectral density revealed a clear periodicity of the maximum precipitation. For precipitation with t = 60 min, the maximum values occur every 9 years, but also shorter periods (3-year) may be observed. The PMP values calculated for Cracow differ significantly from the values calculated using the probability distribution, as well as from the ones observed and they increase with increasing precipitation duration. The differences between the PMP and probable as well as observed precipitation tend to decrease with increasing duration of precipitation.

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