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A Bayes Analysis of Random Walk Model Under Different Error Assumptions

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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.

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Data Availability

The data that support the findings of this study are available from the website http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm.

Code Availability

The code used in this work can be made available upon reasonable request from the corresponding author.

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Acknowledgements

The authors wish to express their thankfulness to the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions that improved the earlier version of the manuscript.

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No funding was received for conducting this study.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Banasthali Vidyapith, Tonk, Rajasthan, 304022, India

    Praveen Kumar Tripathi & Manika Agarwal

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  1. Praveen Kumar Tripathi
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  2. Manika Agarwal
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Contributions

The two authors have equally contributed to this study in each dimension of the paper. The idea and methodology were developed by the first author and is discussed simultaneously with the second/corresponding author. The second author has contributed in the data analysis, coding, and report writing which has been verified and revised by the Dr. Praveen Kumar Tripathi.

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Correspondence to Manika Agarwal.

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Tripathi, P.K., Agarwal, M. A Bayes Analysis of Random Walk Model Under Different Error Assumptions. Ann. Data. Sci. (2023). https://doi.org/10.1007/s40745-023-00465-5

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