Prediction Distribution for Simultaneous Auto-Regressive Model with Multivariate Student-T Error under the Bayesian Approach

Md. Idris Ali; Md. Shajedul Islam; Md. Ahsan Ahamed

doi:10.36948/ijfmr.2023.v05i01.1227

Prediction Distribution for Simultaneous Auto-Regressive Model with Multivariate Student-T Error under the Bayesian Approach

Author(s)	Md. Idris Ali, Md. Shajedul Islam, Md. Ahsan Ahamed
Country	Bangladesh
Abstract	Prediction distribution is a basis for predictive inferences applied in many real world situations. The Bayesian approach under uniform prior is employed in this paper to derive the prediction distribution for Simultaneous Auto-regressive model with multivariate Student-t error distribution. Conditional on a set of realized responses, a single and a set of future responses have a univariate and multivariate Student-t distributions respectively, whose degrees of freedom depend on the size of the realized sample and the dimension of the auto-regression parameters' vector but do not depend on the degrees of freedom of the error distribution. Results are identical to those obtained under normal error distribution by a range of statistical approaches such as the normal distribution, autocorrelations and classical methods. This indicates not only the inference robustness with respect to departures from normal error to multivariate Student-t error distributions, but also indicates that the Bayesian approach with uniform prior is competitive with other statistical methods in the derivation of prediction distribution.
Keywords	Key words: Student’s t-distribution, Chi-square distribution, F-distribution, Auto-regressive model.
Field	Mathematics > Statistics
Published In	Volume 5, Issue 1, January-February 2023
Published On	2023-01-21
Cite This	Prediction Distribution for Simultaneous Auto-Regressive Model with Multivariate Student-T Error under the Bayesian Approach - Md. Idris Ali, Md. Shajedul Islam, Md. Ahsan Ahamed - IJFMR Volume 5, Issue 1, January-February 2023. DOI 10.36948/ijfmr.2023.v05i01.1227
DOI	https://doi.org/10.36948/ijfmr.2023.v05i01.1227
Short DOI	https://doi.org/grpdrk

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Prediction Distribution for Simultaneous Auto-Regressive Model with Multivariate Student-T Error under the Bayesian Approach

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