Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO&lt;sub&gt;2&lt;/sub&gt; Emission Data

Suparman Suparman,Idrus Alhaddad,Tedy Machmud,Fitriana Ibrahim,Hery Suharna,Yahya Hairun,Mahyudin Ritonga,Mohd Saifullah Rusiman

doi:10.13189/ms.2022.100203

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 CO<sub>2</sub> emission data. The results of this paper can be applied to modeling and forecasting confidential data in various sectors.

Highlights

The noise present in the AR model is in the form of additives, while in some literature such as [3], it is assumed to have a Gaussian or normal distribution
Exponential noise [5], and Laplace noise [6]. These models do not protect confidential data when the research results are published in a scientific journal, an additional method known as variable transformation is needed to secure the data
These results indicate that the reversible jump Markov Chain Monte Carlo (MCMC) algorithm can accurately estimate the parameters of the Laplacian AR model

Summary

Introduction

Autoregressive (AR) is a stochastic mathematical model used for forecasting and pattern recognition. According to [1] [2], the understanding and characteristics of this model are widely used in various fields, such as time series and signal processing. For wider usage, models have been developed to be in addition to a normal distribution, such as Pareto noise [4], model AR exponential noise [5], and Laplace noise [6]. These models do not protect confidential data when the research results are published in a scientific journal, an additional method known as variable transformation is needed to secure the data

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