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 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 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 Comparison of Feedforward and Recurrent Neural Network in Forecasting Chaotic Dynamical System

2019 ◽  
Vol 10 (37) ◽  
pp. 31-44
Author(s):  
Engin Kandıran ◽  
Avadis Hacınlıyan
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Time Series ◽  
Function Approximation ◽  
Feedforward Neural Network ◽  
Network Architectures ◽  
Chaotic Dynamical System ◽  
Global Function ◽  
The Neural Network ◽  
Hidden Layer

Artificial neural networks are commonly accepted as a very successful tool for global function approximation. Because of this reason, they are considered as a good approach to forecasting chaotic time series in many studies. For a given time series, the Lyapunov exponent is a good parameter to characterize the series as chaotic or not. In this study, we use three different neural network architectures to test capabilities of the neural network in forecasting time series generated from different dynamical systems. In addition to forecasting time series, using the feedforward neural network with single hidden layer, Lyapunov exponents of the studied systems are forecasted.

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.

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