Bayesian Skew Normal Seemingly Unrelated Regression Modelling of Gross Regional Domestic Product

Agus Budi Santosa,Nur Iriawan,Setiawan Setiawan,Mohammad Dokhi

doi:10.18187/pjsor.v14i4.2359

Agus Budi Santosa, Nur Iriawan + Show 2 more

Open Access

https://doi.org/10.18187/pjsor.v14i4.2359

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Abstract

The assumption of the error normality in the regression model was often questioned especially in cases where there was an outlier, which causes the behavior of asymmetric data. To overcome this, without data transformation, we could use skew distribution. This distribution was very important and applicable in various fields of science such as finance, economics, actuarial science, medicine, biology, investment. Skew Normal distributions had been proven to have a convenient for calculating bias in data with asymmetric behavior. This study aims to model SUR with Skew Normal error using Bayesian approach applied to East Java GRDP data. This study would compared two types of models, namely models with Normal distributed errors and models with Skew Normal distributed errors. The result of parameter estimation with Bayesian approach shows that SUR Skew Normal model was more suitable for East Java GRDP modeling rather than using normal error model. This was based on their smaller Root of Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) value.Â

Highlights

In several economic and other areas of knowledge, the seemingly unrelated regression (SUR) model introduced by Zellner (1962) was often used as a tool to explain the occurrence of an economic phenomenon
The Skew Normal distribution which was made by Azzalini, able to provide the relaxation of normality as a pattern that was tilted to the right or tilted to the left, but unable to maintain its stability in its location or stable in the mean (Iriawan, 2012)
Comparing the goodness of a model based on several criteria for selecting the model (RMSE, Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE)) shows that the Markov Chain Monte Carlo (MCMC) Skew Normal approach was better than the MCMC Normal approach

Summary

Introduction

In several economic and other areas of knowledge, the seemingly unrelated regression (SUR) model introduced by Zellner (1962) was often used as a tool to explain the occurrence of an economic phenomenon. The Skew Normal distribution which was made by Azzalini, able to provide the relaxation of normality as a pattern that was tilted to the right or tilted to the left, but unable to maintain its stability in its location or stable in the mean (Iriawan, 2012). This means that if the pattern of a residual data was detected rather tilted to the right, the modeling must bear the shift of its residual center shifted to the right which was no longer centered in its mode location at zero. The assumptions of Normal and Skew-Normal errors would be employed to be coupled with the Bayesian approach and the MCMC method for estimating the parameters

Multivariate Skew Normal Distribution

Bayes SUR Skew Normal Model

Findings

Conclusion