Mathematics and Statistics Vol. 10(2), pp. 301 - 307
DOI: 10.13189/ms.2022.100203
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Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO₂ Emission Data

Suparman ^1,*, Hery Suharna ², Mahyudin Ritonga ³, Fitriana Ibrahim ², Tedy Machmud ⁴, Mohd Saifullah Rusiman ⁵, Yahya Hairun ², Idrus Alhaddad ^2
1 Faculty of Teacher Training and Education, Universitas Ahmad Dahlan, Indonesia
² Faculty of Teacher Training and Education, Universitas Khairun, Ternate, Indonesia
³ Faculty of Islamic Studies, Muhammadiyah University of West Sumatera, Padang, Indonesia
⁴ Faculty of Mathematics and Sciences, Universitas Negeri Gorontalo, Gorontalo, Indonesia
⁵ Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Malaysia

ABSTRACT

Autoregressive (AR) model is applied to model various types of data. For confidential data, data confusion is very important to protect the data from being known by other unauthorized parties. This paper aims to find data modeling with transformations in the AR model. In this AR model, the noise has a Laplace distribution. AR model parameters include order, coefficients, and variance of the noise. The estimation of the AR model parameter is proposed in a Bayesian method by using the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. This paper shows that the posterior distribution of AR model parameters has a complicated equation, so the Bayes estimator cannot be determined analytically. Bayes estimators for AR model parameters are calculated using the reversible jump MCMC algorithm. This algorithm was validated through a simulation study. This algorithm can accurately estimate the parameters of the transformed AR model with Laplacian noise. This algorithm produces an AR model that satisfies the stationary conditions. The novelty in this paper is the use of transformations in the Laplacian AR model to secure research data when the research results are published in a scientific journal. As an example application, the Laplacian AR model was used to model CO₂ emission data. The results of this paper can be applied to modeling and forecasting confidential data in various sectors.

KEYWORDS
Autoregressive Processes, Bayes Methods, CO₂ Emission, Laplacian Noise, Monte Carlo Methods

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Suparman , Hery Suharna , Mahyudin Ritonga , Fitriana Ibrahim , Tedy Machmud , Mohd Saifullah Rusiman , Yahya Hairun , Idrus Alhaddad , "Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO₂ Emission Data," Mathematics and Statistics, Vol. 10, No. 2, pp. 301 - 307, 2022. DOI: 10.13189/ms.2022.100203.

(b). APA Format:
Suparman , Hery Suharna , Mahyudin Ritonga , Fitriana Ibrahim , Tedy Machmud , Mohd Saifullah Rusiman , Yahya Hairun , Idrus Alhaddad (2022). Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO₂ Emission Data. Mathematics and Statistics, 10(2), 301 - 307. DOI: 10.13189/ms.2022.100203.