scholarly journals THE HYPOTHESIS TEST OF COVARIATION FUNCTIONS OF QUASIPERIODIC PROCESSES SYSTEMS REPRESENTED BY CYLINDRICAL IMAGE MODELS

2020 ◽  
Vol 62 (4) ◽  
pp. 93-102
Author(s):  
Viktor R. Krasheninnikov ◽  
◽  
Iulia E. Kuvaiskova ◽  
Olga E. Malenova ◽  
Aleksei Iu. Subbotin ◽  
...  
Keyword(s):  
Time Series ◽  
Hypothesis Test ◽  
Random Processes ◽  
Model Parameters ◽  
Sea Waves ◽  
Process Systems ◽  
System A ◽  
Image Models ◽  
Parameter Values ◽  
The Given

The generally accepted mathematical model of a wide variety of natural, technical, economic and other objects that exist in time are random processes, for example sea waves, wind, vibrations of engines and hydraulic units, biorhythms, etc. An object is usually described by several parameters, that is a system of random processes or time series. The processes occurring in many objects have a form close to periodic – quasiperiodic, namely there is a periodicity with an element of unpredictability, for example speech sounds, vibrations of various technical objects, daily temperature fluctuations, etc. In order to formulate the problems of processing the quasiperiodic process systems, their mathematical models are required. For this purpose, authors propose models in which the processes are presented in the form of spiral sweeps on autoregressive cylindrical images. A suitable set of parameter values for these models provides a given degree of quasiperiodicity of individual processes and the given covariance relationships between the processes of the system. A criterion is proposed for testing the hypotheses about the correspondence of the observed system of time series to their model of the described type. The authors provide the examples of the application of this criterion with an analysis of the sensitivity to deviations of the model parameters from the expected ones are given.

Multivariate Time Series Decomposition into Oscillation Components

2017 ◽  
Vol 29 (8) ◽  
pp. 2055-2075 ◽  
Author(s):  
Takeru Matsuda ◽  
Fumiyasu Komaki
Keyword(s):  
Time Series ◽  
Empirical Bayes ◽  
Multivariate Time Series ◽  
Phase Relationship ◽  
Information Criterion ◽  
Model Parameters ◽  
Phase Dynamics ◽  
Univariate Time Series ◽  
Linear State ◽  
The Given

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

Structural health monitoring by probability density function of autoregressive-based damage features and fast distance correlation method

2021 ◽  
pp. 107754632110201
Author(s):  
Mohammad Ali Heravi ◽  
Seyed Mehdi Tavakkoli ◽  
Alireza Entezami
Keyword(s):  
Time Series ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Large Scale ◽  
Hypothesis Test ◽  
Correlation Method ◽  
Model Parameters ◽  
Density Estimator ◽  
Distance Correlation

In this article, the autoregressive time series analysis is used to extract reliable features from vibration measurements of civil structures for damage diagnosis. To guarantee the adequacy and applicability of the time series model, Leybourne–McCabe hypothesis test is used. Subsequently, the probability density functions of the autoregressive model parameters and residuals are obtained with the aid of a kernel density estimator. The probability density function sets are considered as damage-sensitive features of the structure and fast distance correlation method is used to make decision for detecting damages in the structure. Experimental data of a well-known three-story laboratory frame and a large-scale bridge benchmark structure are used to verify the efficiency and accuracy of the proposed method. Results indicate the capability of the method to identify the location and severity of damages, even under the simulated operational and environmental variability.

scholarly journals Rainfall prediction climatological station of Banjarbaru using arima kalman filter

2021 ◽  
Vol 2106 (1) ◽  
pp. 012003
Author(s):  
W A Mehta ◽  
Y Sukmawaty ◽  
Khairullah
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Time Series Analysis ◽  
Arima Model ◽  
Training Data ◽  
Actual Data ◽  
Model Parameters ◽  
Rainfall Prediction ◽  
Series Analysis ◽  
Parameter Values

Abstract Time series analysis is a method built in a particular time sequence for prediction. One of the models in time series analysis used for prediction is the ARIMA model introduced by Box and Jenkins. As time goes by, the ARIMA model was developed by applying algorithms, one of which was the Kalman Filter algorithm. This study aims to estimate the parameters of the ARIMA model used as the Kalman Filter’s initial value to forecast rainfall using ARIMA and ARIMA Kalman Filter. Determination of the ARIMA model is done by dividing the data into training and testing. The results obtained from the three training data have the same model, namely ARIMA (0,0,0) × (0,1,1)12 models but with different parameter values than those used as initial values for the Kalman Filter. The results obtained using the ARIMA model with Kalman Filter significantly affect the initial data of 90% training data model parameters with an RMSE value of 155,13. Then predictions are made, the results obtained by ARIMA Kalman Filter can follow the actual data, but from June to October, the prediction results cannot approach the actual data. According to events in the field, June to October is the dry season, where rainfall is deficient

scholarly journals Estimating parameters from multiple time series of population dynamics using Bayesian inference

2018 ◽  
Author(s):  
Benjamin Rosenbaum ◽  
Michael Raatz ◽  
Guntram Weithoff ◽  
Gregor F. Fussmann ◽  
Ursula Gaedke
Keyword(s):  
Time Series ◽  
Population Dynamics ◽  
Bayesian Inference ◽  
Steady States ◽  
Series Data ◽  
Model Parameters ◽  
List Type ◽  
Model Predictions ◽  
Cyclic Dynamics ◽  
Parameter Values

AbstractEmpirical time series of interacting entities, e.g. species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations.In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics.Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics.By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.

scholarly journals On a new four-dimensional model of memristor-based chaotic circuit in the context of nonsingular Atangana–Baleanu–Caputo operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chernet Tuge Deressa ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
System Analysis ◽  
Phase Portraits ◽  
Banach Fixed Point Theorem ◽  
Memory Element ◽  
System A ◽  
Trivial Equilibrium ◽  
Computational Circuits ◽  
Parameter Values ◽  
The Given

AbstractA memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A four-dimensional memristor system with the Atangana–Baleanu fractional nonsingular operator in the sense of Caputo is investigated. The Banach fixed point theorem for contraction principle is used to verify the existence–uniqueness of the fractional representation of the given system. A newly developed numerical scheme for fractional-order systems introduced by Toufik and Atangana is utilized to obtain the phase portraits of the suggested system for different fractional derivative orders and different parameter values of the system. Analysis on the local stability of the fractional model via the Matignon criteria showed that the trivial equilibrium point is unstable. The dynamics of the system are investigated using Lyapunov exponents for the characterization of the nature of the chaos and to verify the dissipativity of the system. It is shown that the supposed system is chaotic and it is significantly sensitive to parameter variation and small initial condition changes.

Modeling Multivariate Time Series on Manifolds with Skew Radial Basis Functions

2011 ◽  
Vol 23 (1) ◽  
pp. 97-123 ◽  
Author(s):  
Arta A. Jamshidi ◽  
Michael J. Kirby
Keyword(s):  
Time Series ◽  
Radial Basis Functions ◽  
Ad Hoc ◽  
Hypothesis Test ◽  
Basis Functions ◽  
Statistical Hypothesis ◽  
Model Parameters ◽  
Validation Data ◽  
Accuracy Order ◽  
Radial Basis

We present an approach for constructing nonlinear empirical mappings from high-dimensional domains to multivariate ranges. We employ radial basis functions and skew radial basis functions for constructing a model using data that are potentially scattered or sparse. The algorithm progresses iteratively, adding a new function at each step to refine the model. The placement of the functions is driven by a statistical hypothesis test that accounts for correlation in the multivariate range variables. The test is applied on training and validation data and reveals nonstatistical or geometric structure when it fails. At each step, the added function is fit to data contained in a spatiotemporally defined local region to determine the parameters—in particular, the scale of the local model. The scale of the function is determined by the zero crossings of the autocorrelation function of the residuals. The model parameters and the number of basis functions are determined automatically from the given data, and there is no need to initialize any ad hoc parameters save for the selection of the skew radial basis functions. Compactly supported skew radial basis functions are employed to improve model accuracy, order, and convergence properties. The extension of the algorithm to higher-dimensional ranges produces reduced-order models by exploiting the existence of correlation in the range variable data. Structure is tested not just in a single time series but between all pairs of time series. We illustrate the new methodologies using several illustrative problems, including modeling data on manifolds and the prediction of chaotic time series.

Construct Validity

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Construct Validity ◽  
Hypothesis Test ◽  
Secondary Data ◽  
Time Frame ◽  
Primary Data ◽  
Optimal Time ◽  
Intervention Model ◽  
Right Hand ◽  
The Right

Chapter 8 focuses on threats to construct validity arising from the left-hand side time series and the right-hand side intervention model. Construct validity is limited to questions of whether an observed effect can be generalized to alternative cause and effect measures. The “talking out” self-injurious behavior time series, shown in Chapter 5, are examples of primary data. Researchers often have no choice but to use secondary data that were collected by third parties for purposes unrelated to any hypothesis test. Even in those less-than-ideal instances, however, an optimal time series can be constructed by limiting the time frame and otherwise paying attention to regime changes. Threats to construct validity that arise from the right-hand side intervention model, such as fuzzy or unclear onset and responses, are controlled by paying close attention to the underlying theory. Even a minimal theory should specify the onset and duration of an impact.

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

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