Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

Ferreira, Guillermo; Navarrete, Jean P.; Rodríguez‐Cortés, Francisco J.; Mateu, Jorge

doi:10.1080/00949655.2017.1334778

Cited by 7 publications

(8 citation statements)

References 34 publications

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“…Note that the RMSE of the three filters are of the same order of the corresponding [P(r r)] ii . This is the expected behaviour in order to satisfy the second consistency condition (24). However, for the CKF the RMSE of the coefficients slightly depart from their corresponding [P(r r)] ii .…”

Section: Filter Consistencymentioning

confidence: 63%

“…However, they are estimated recursively with a maximum‐likelihood procedure, numerically solved by means of a steepest descent method that updates the likelihood function gradient as new samples arrive, in order to keep a low computational load [23]. Recently, [24] proposed estimating GARCH time‐varying parameters via the Kalman filter recursive equations, adapting the state‐space representation of [20] to non‐stationary GARCH models.…”

Section: Introductionmentioning

confidence: 99%

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Non‐linear Kalman filters comparison for generalised autoregressive conditional heteroscedastic clutter parameter estimation

Pascual

von-Ellenrieder

Areta

et al. 2019

IET signal process.

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In this work, the authors analyse the estimation of the generalised autoregressive conditional heteroscedastic (GARCH) process conditional variance based on three non-linear filtering approaches: extended Kalman filter (EKF), unscented Kalman filter and cubature Kalman filter. The authors present a state model for a GARCH process and derive an EKF including second-order non-linear terms for simultaneous estimation of state and parameters. Using synthetic data, the authors evaluate the consistency and the correlation of the innovations for the three filters, by means of numerical simulations. The authors also study the performance of smoothed versions of the non-linear Kalman filters using real clutter data in comparison with a conventional quasi-maximum likelihood estimation method for the GARCH process coefficients. The authors show that with all methods the process coefficients estimates are of the same order and the resulting conditional variances are commensurable. However, the non-linear Kalman filters greatly reduce the computational load. These kind of filters could be used for the radar detector based on a GARCH clutter model that uses an adaptive threshold that demands the conditional variance at each decision instant.

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Section: Filter Consistencymentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Non‐linear Kalman filters comparison for generalised autoregressive conditional heteroscedastic clutter parameter estimation

Pascual

von-Ellenrieder

Areta

et al. 2019

IET signal process.

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show abstract

“…We call our method time-varying Bayesian Integer valued Generalized Auto Regressive Conditional Heteroscedastic (TVBINGARCH) model. We impose following constraints on the parameter space similar to [18],…”

Section: Time-varying Generalized Autoregressive Conditional Heteroscedasticity Model For Countsmentioning

confidence: 99%

“…This constraint ensures a unique solution of the time-varying GARCH process as discussed in [14,38,18]. Now, we put priors on the functions μ(•), a i (•) and b j (•) such that they are supported in P 1 .…”

Section: Time-varying Generalized Autoregressive Conditional Heteroscedasticity Model For Countsmentioning

confidence: 99%

Time-varying auto-regressive models for count time-series

Roy

Karmakar

2021

Electron. J. Statist.

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Count-valued time series data are routinely collected in many application areas. We are particularly motivated to study the count time series of daily new cases, arising from the COVID-19 spread. First, we propose a Bayesian framework to study the time-varying semiparametric AR(p) model for the count and then extend it to a more sophisticated time-varying INGARCH model. We calculate posterior contraction rates of the proposed Bayesian methods with respect to the average Hellinger metric. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We substantiate our methods by simulations that show superiority compared to some of the existing methods that closely fit this setting. Finally, we analyze the daily time series data of newly confirmed cases in NYC to study the spread of COVID for three months.

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Section: Time-varying Generalized Autoregressive Conditional Heterosc...mentioning

confidence: 99%

Time-varying auto-regressive models for count time-series

Roy¹,

Karmakar²

2020

Preprint

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Count-valued time series data are routinely collected in many application areas. We are particularly motivated to study the count time series of daily new cases, arising from COVID-19 spread. First, we propose a Bayesian framework to study time-varying semiparametric AR(p) model for count and then extend it to propose a time-varying INGARCH model considering the rapid changes in the spread. We calculate posterior contraction rates of the proposed Bayesian methods with respect to average Hellinger metric. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We substantiate our methods by simulations that show superiority compared to some of the close existing methods. Finally we analyze the daily time series data of newly confirmed cases to study its spread through different government interventions.

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Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

Cited by 7 publications

References 34 publications

Non‐linear Kalman filters comparison for generalised autoregressive conditional heteroscedastic clutter parameter estimation

Non‐linear Kalman filters comparison for generalised autoregressive conditional heteroscedastic clutter parameter estimation

Time-varying auto-regressive models for count time-series

Time-varying auto-regressive models for count time-series

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