Bayesian estimation of an autoregressive model using Markov chain Monte Carlo

Barnett, Glen; Kohn, Robert; Sheather, Simon J.

doi:10.1016/0304-4076(95)01744-5

Cited by 92 publications

(74 citation statements)

References 18 publications

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“…Although the results will be different with different prior settings, more or less, the results presented here give us an impression of how the Bayesian AR model averaging approach performs on time series forecasting. See Barnett, Kohn and Sheather (1996) for an alternative method for Bayesian AR model estimation.…”

Section: Forecasting Performancementioning

confidence: 99%

Bayesian neural networks for nonlinear time series forecasting

Liang

2005

Stat Comput

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In this article, we apply Bayesian neural networks (BNNs) to time series analysis, and propose a Monte Carlo algorithm for BNN training. In addition, we go a step further in BNN model selection by putting a prior on network connections instead of hidden units as done by other authors. This allows us to treat the selection of hidden units and the selection of input variables uniformly. The BNN model is compared to a number of competitors, such as the Box-Jenkins model, bilinear model, threshold autoregressive model, and traditional neural network model, on a number of popular and challenging data sets. Numerical results show that the BNN model has achieved a consistent improvement over the competitors in forecasting future values. Insights on how to improve the generalization ability of BNNs are revealed in many respects of our implementation, such as the selection of input variables, the specification of prior distributions, and the treatment of outliers.

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Section: Forecasting Performancementioning

confidence: 99%

Bayesian neural networks for nonlinear time series forecasting

Liang

2005

Stat Comput

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“…The development of AR models with non-Gaussian excitation has a relatively long history. Work presented in [3]- [5] utilizes essentially the same model as we discuss here. In these papers, the issue of parameter inference is rightly tackled with a fully Bayesian approach using Markov chain Monte Carlo (MCMC) sampling methods.…”

Section: Introductionmentioning

confidence: 99%

“…The likelihood of a data point is given by the mixture model (2) where is an indicator variable indicating which component of the noise mixture model is selected at presentation of the th datum. These are chosen probabilistically according to (3) The joint likelihood of a data point and indicator variable is (4) which, given that the noise samples are assumed independent and identically distributed, gives (5) over the whole date set, where T and T . Each component in the noise model is a Gaussian, and hence (6)…”

Section: Generalized Autoregressive Modelsmentioning

confidence: 99%

Variational Bayes for generalized autoregressive models

Roberts

Penny

2002

IEEE Trans. Signal Process.

136

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Abstract-We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model-order selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encouraging results.Index Terms-Bayesian inference, generalized autoregressive models, model order selection, robust estimation.

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“…Monahan (1983) introduced a numerical integration algorithm in order to calculate the posterior probabilities for the orders of ARMA models. Moreover, the MCMC methods were used by Barnett et al (1996) to estimate the order of AR processes and by Philippe (2006) to estimate the orders of ARMA models.…”

Section: Review Of the Literaturementioning

confidence: 99%

On Bayesian Identification of Autoregressive Processes

Soliman

Shaarawy²,

Sorour³

2015

Pak.j.stat.oper.res.

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The main objective of the current study is to handle the identification problem of autoregressive processes from the Bayesian point of view. Two Bayesian identification approaches are considered. They are referred to as the direct and the indirect approaches. The two approaches are employed to solve the Bayesian identification problem of autoregressive processes using three well known priors. These priors are the G prior, the Natural-Conjugate prior and Jeffrey's prior. The theoretical derivations related to the two Bayesian identification approaches are conducted using the above mentioned priors. Moreover, the performance of the two techniques, using each of the three priors, is investigated via comprehensive simulation studies. Simulation results show that the two techniques are adequate to solve the identification problem of autoregressive processes. The increase in the time series length leads to better performance for each technique. The use of different priors doesn't affect the numerical results.

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Bayesian estimation of an autoregressive model using Markov chain Monte Carlo

Cited by 92 publications

References 18 publications

Bayesian neural networks for nonlinear time series forecasting

Bayesian neural networks for nonlinear time series forecasting

Variational Bayes for generalized autoregressive models

On Bayesian Identification of Autoregressive Processes

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