scholarly journals Estimating eigenvalues of dynamical systems from time series with applications to predicting cardiac alternans

2012 ◽  
Vol 468 (2147) ◽  
pp. 3649-3666 ◽  
Author(s):  
Adam Petrie ◽  
Xiaopeng Zhao
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Data Driven ◽  
Standard Errors ◽  
Statistical Techniques ◽  
Likelihood Methods ◽  
Maximum Likelihood Methods ◽  
The Usa ◽  
Cardiac Alternans ◽  
The Stability

The stability of a dynamical system can be indicated by eigenvalues of its underlying mathematical model. However, eigenvalue analysis of a complicated system (e.g. the heart) may be extremely difficult because full models may be intractable or unavailable. We develop data-driven statistical techniques, which are independent of any underlying dynamical model, that use principal components and maximum-likelihood methods to estimate the dominant eigenvalues and their standard errors from the time series of one or a few measurable quantities, e.g. transmembrane voltages in cardiac experiments. The techniques are applied to predicting cardiac alternans that is characterized by an eigenvalue approaching −1. Cardiac alternans signals a vulnerability to ventricular fibrillation, the leading cause of death in the USA.

scholarly journals Estimating the real burden of disease under a pandemic situation: The SARS-CoV2 case

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242956 ◽  
Author(s):  
Amanda Fernández-Fontelo ◽  
David Moriña ◽  
Alejandra Cabaña ◽  
Argimiro Arratia ◽  
Pere Puig
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Severe Acute Respiratory Syndrome ◽  
Hidden Markov ◽  
Time Dependent ◽  
Likelihood Methods ◽  
Count Time Series ◽  
Maximum Likelihood Methods ◽  
Hidden Layer ◽  
Reported Data

The present paper introduces a new model used to study and analyse the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration process with Poisson immigration, Po-INAR(1), together with a mechanism that allows the estimation of the under-reporting in non-stationary count time series. A novelty of the model is that the expectation of the unobserved process’s innovations is a time-dependent function defined in such a way that information about the spread of an epidemic, as modelled through a Susceptible-Infectious-Removed dynamical system, is incorporated into the model. In addition, the parameter controlling the intensity of the under-reporting is also made to vary with time to adjust to possible seasonality or trend in the data. Maximum likelihood methods are used to estimate the parameters of the model.

scholarly journals Selecting between causal and noncausal models with quantile autoregressions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alain Hecq ◽  
Li Sun
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Latin American ◽  
Financial Time Series ◽  
Selection Criterion ◽  
Likelihood Methods ◽  
Approximate Maximum Likelihood ◽  
Financial Time ◽  
Maximum Likelihood Methods ◽  
Latin American Countries

AbstractWe propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations in QAR. This new modelling perspective is appealing for investigating the presence of bubbles in economic and financial time series, and is an alternative to approximate maximum likelihood methods. We illustrate our analysis using hyperinflation episodes of Latin American countries.

scholarly journals Contractibility of a persistence map preimage

2020 ◽  
Vol 4 (4) ◽  
pp. 509-523
Author(s):  
Jacek Cyranka ◽  
Konstantin Mischaikow ◽  
Charles Weibel
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Time Series ◽  
Data Driven ◽  
Dimensional System ◽  
Multiple Time ◽  
Multiple Time Series ◽  
Topological Features ◽  
Persistence Diagram ◽  
Persistence Diagrams

Abstract This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of snapshots of solutions, what conclusions can be drawn about solutions of the original dynamical system? We address this challenge in the context of an N dimensional system of ordinary differential equation defined in $${\mathbb {R}}^N$$ R N . To each point in $${\mathbb {R}}^N$$ R N (e.g. an initial condition) we associate a persistence diagram. The main result of this paper is that under this association the preimage of every persistence diagram is contractible. As an application we provide conditions under which multiple time series of persistence diagrams can be used to conclude the existence of a fixed point of the differential equation that generates the time series.

The Application Of Statistical Techniques To Insulation Aging Test

1983 ◽  
pp. 67-85
Author(s):  
Hussein Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Statistical Techniques ◽  
Test Results ◽  
Likelihood Methods ◽  
Methods Comparison ◽  
Insulating Materials ◽  
Insulation Aging ◽  
Aging Test ◽  
Maximum Likelihood Methods ◽  
Statistical Variance

Kertas kerja int membentangkan cara-eara untuk mendapatkan maklumat hayat dan daya ketahanan sesuatu penebat. Maklumat dan data-data yang diperolehi masih lagi dalam keraguan atau belum boleh dibuar ketetapan disebabkan oleh perselisihan perangkaan pada keputusan ujian, justeru itu keputusan daripada ujian-ujian dinilai dengan menggunakan kaedah-kaedah perangkaan. Kaedah-kaedah ini ialah grafik dan kebolehjadian maksima. Dibentangkan juga di sini perbandingan di antara kedua-dua kaedah tersebut. Bahan penebat padat yang digunakan untuk ujikaji ini adalah polychloroprene (P.V.C) dan polypropylene. In this paper, methods for obtaining the information on the life and endurance of the insulating materials are presented. The information obtained is compounded by uncertainties due to statistical variance of the test results, hence the results of the tests are therefore evaluated by statistical techniques. These methods are known as graphical and Maximum Likelihood methods. Comparison between the two methods are presented here. The solid insulating materials subjected to test are polychloroprene (P.V.C.) and polypropylene.

scholarly journals The geoengineering approach to the study of rivers and reservoirs

2019 ◽  
Vol 488 (1) ◽  
pp. 1-13
Author(s):  
Patrick W. M. Corbett ◽  
Amanda Owen ◽  
Adrian J. Hartley ◽  
Sila Pla-Pueyo ◽  
Daniel Barreto ◽  
...  
Keyword(s):  
Time Series ◽  
Statistical Techniques ◽  
Government Agencies ◽  
Short Term ◽  
Geological Record ◽  
Global Sustainability ◽  
Spatial Sense ◽  
The Usa ◽  
Impacts Of Human Activity ◽  
Rivers And Reservoirs

AbstractThis Special Publication contains contributions for two meetings held to explore the links between geoscience and engineering in rivers and reservoirs (surface and subsurface). The first meeting was held in Brazil and, as a result, the volume contains many contributions from Brazil. The second was held in Edinburgh, and produced contributions from modern rivers in the USA, China, India and Scotland. The geological record from Carboniferous to Recent is represented. A range of outcrop techniques are presented along with statistical techniques used to identify patterns in the time series and spatial sense. The book is intended to cover the cross-disciplinary interest in rivers and their sediments, and will interest geologists, geomorphologists, civil, geotechnical and petroleum engineers, and government agencies. Some of the papers collected here demonstrate longer term impacts of human activity on rivers and how these might change the future geological record and, more importantly in the short term, impact on the UN Global Sustainability Goals.

scholarly journals Financial time series volatility analysis using Gaussian process state-space models

2021 ◽  
Author(s):  
Jianan Han
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
State Space ◽  
Financial Time Series ◽  
State Space Model ◽  
Likelihood Methods ◽  
Nonparametric Modeling ◽  
Space Model ◽  
Financial Time ◽  
Maximum Likelihood Methods

In this thesis, we propose a novel nonparametric modeling framework for financial time series data analysis, and we apply the framework to the problem of time varying volatility modeling. Existing parametric models have a rigid transition function form and they often have over-fitting problems when model parameters are estimated using maximum likelihood methods. These drawbacks effect the models' forecast performance. To solve this problem, we take Bayesian nonparametric modeling approach. By adding Gaussian process prior to the hidden state transition process, we extend the standard state-space model to a Gaussian process state-space model. We introduce our Gaussian process regression stochastic volatility (GPRSV) model. Instead of using maximum likelihood methods, we use Monte Carlo inference algorithms. Both online particle filter and offline particle Markov chain Monte Carlo methods are studied to learn the proposed model. We demonstrate our model and inference methods with both simulated and empirical financial data.

scholarly journals Financial time series volatility analysis using Gaussian process state-space models

2021 ◽  
Author(s):  
Jianan Han
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
State Space ◽  
Financial Time Series ◽  
State Space Model ◽  
Likelihood Methods ◽  
Nonparametric Modeling ◽  
Space Model ◽  
Financial Time ◽  
Maximum Likelihood Methods

In this thesis, we propose a novel nonparametric modeling framework for financial time series data analysis, and we apply the framework to the problem of time varying volatility modeling. Existing parametric models have a rigid transition function form and they often have over-fitting problems when model parameters are estimated using maximum likelihood methods. These drawbacks effect the models' forecast performance. To solve this problem, we take Bayesian nonparametric modeling approach. By adding Gaussian process prior to the hidden state transition process, we extend the standard state-space model to a Gaussian process state-space model. We introduce our Gaussian process regression stochastic volatility (GPRSV) model. Instead of using maximum likelihood methods, we use Monte Carlo inference algorithms. Both online particle filter and offline particle Markov chain Monte Carlo methods are studied to learn the proposed model. We demonstrate our model and inference methods with both simulated and empirical financial data.

NOISE REDUCTION BY GRADIENT DESCENT

1993 ◽  
Vol 03 (01) ◽  
pp. 113-118 ◽  
Author(s):  
MIKE DAVIES
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Gradient Descent ◽  
Nonlinear Dynamical System ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Gradient Descent Method ◽  
Local Minima ◽  
Nonlinear Dynamical ◽  
The Stability

The problem of reducing noise in a time series from a nonlinear dynamical system can be formulated as a nonlinear minimisation process. This paper demonstrates that this can be easily solved using a steepest descent method without any of the stability problems that have been associated with using a Newton method [Hammel, 1990; Farmer & Sidorowich, 1991]. The optimisation function to be minimised is also shown not to contain any local minima if the trajectory is always hyperbolic. So that in this case this method will converge eventually to a purely deterministic trajectory. Finally this method is compared with a recently proposed algorithm [Schreiber & Grassberger, 1991], which can be viewed as an alternative gradient descent method.

DEVELOPMENT OF STREAMFLOW DROUGHT INDICES IN THE MORAVA RIVER BASIN

2020 ◽  
Author(s):  
Ondrej Ledvinka ◽  
◽  
Pavel Coufal ◽  
Keyword(s):  
Time Series ◽  
Kendall Test ◽  
Drought Indices ◽  
Drought Period ◽  
Left Hand ◽  
Low Flows ◽  
Current Period ◽  
Catchment Size ◽  
Morava River ◽  
The Stability

The territory of Czechia currently suffers from a long-lasting drought period which has been a subject of many studies, including the hydrological ones. Previous works indicated that the basin of the Morava River, a left-hand tributary of the Danube, is very prone to the occurrence of dry spells. It also applies to the development of various hydrological time series that often show decreases in the amount of available water. The purpose of this contribution is to extend the results of studies performed earlier and, using the most updated daily time series of discharge, to look at the situation of the so-called streamflow drought within the basin. 46 water-gauging stations representing the rivers of diverse catchment size were selected where no or a very weak anthropogenic influences are expected and the stability and sensitivity of profiles allow for the proper measurement of low flows. The selected series had to cover the most current period 1981-2018 but they could be much longer, which was considered beneficial for the next determination of the development direction. Various series of drought indices were derived from the original discharge series. Specifically, 7-, 15- and 30-day low flows together with deficit volumes and their durations were tested for trends using the modifications of the Mann– Kendall test that account for short-term and long-term persistence. In order to better reflect the drivers of streamflow drought, the indices were considered for summer and winter seasons separately as well. The places with the situation critical to the future water resources management were highlighted where substantial changes in river regime occur probably due to climate factors. Finally, the current drought episode that started in 2014 was put into a wider context, making use of the information obtained by the analyses.

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