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A Bayes Analysis of Random Walk Model Under Different Error Assumptions

A Bayes Analysis of Random Walk Model Under Different Error Assumptions In this paper, the Bayesian analyses for the random walk models have been performed under the assumptions of normal distribution, log-normal distribution and the stochastic volatility model, for the error component, one by one. For the various parameters, in each model, some suitable choices of informative and non-informative priors have been made and the posterior distributions are calculated. For the first two choices of error distribution, the posterior samples are easily obtained by using the gamma generating routine in R software. For a random walk model, having stochastic volatility error, the Gibbs sampling with intermediate independent Metropolis–Hastings steps is employed to obtain the desired posterior samples. The whole procedure is numerically illustrated through a real data set of crude oil prices from April 2014 to March 2022. The models are, then, compared on the basis of their accuracies in forecasting the true values. Among the other choices, the random walk model with stochastic volatile errors outperformed for the data in hand. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

A Bayes Analysis of Random Walk Model Under Different Error Assumptions

Tripathi, Praveen Kumar; Agarwal, Manika
Annals of Data Science , Volume OnlineFirst – Apr 22, 2023
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References (44)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-023-00465-5
Publisher site
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Abstract

In this paper, the Bayesian analyses for the random walk models have been performed under the assumptions of normal distribution, log-normal distribution and the stochastic volatility model, for the error component, one by one. For the various parameters, in each model, some suitable choices of informative and non-informative priors have been made and the posterior distributions are calculated. For the first two choices of error distribution, the posterior samples are easily obtained by using the gamma generating routine in R software. For a random walk model, having stochastic volatility error, the Gibbs sampling with intermediate independent Metropolis–Hastings steps is employed to obtain the desired posterior samples. The whole procedure is numerically illustrated through a real data set of crude oil prices from April 2014 to March 2022. The models are, then, compared on the basis of their accuracies in forecasting the true values. Among the other choices, the random walk model with stochastic volatile errors outperformed for the data in hand.

Journal

Annals of Data Science – Springer Journals

Published: Apr 22, 2023

Keywords: Random walk model; Log-normal distribution; Stochastic volatility model; Markov chain Monte Carlo; Gibbs sampler; Metropolis–Hastings algorithm

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