Mathematics and Statistics Vol. 12(2), pp. 167 - 174
DOI: 10.13189/ms.2024.120206
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Forecasts with SPR Model Using Bootstrap-Reversible Jump MCMC

Suparman ^1,*, Eviana Hikamudin ², Hery Suharna ³, Aryanti ², In Hi Abdullah ³, Rina Heryani ^2
1 Faculty of Teacher Training and Education, Universitas Ahmad Dahlan, Indonesia
² Faculty of Education, Universitas Pendidikan Indonesia, Indonesia
³ Faculty of Teacher Training and Education, Universitas Khairun, Indonesia

ABSTRACT

Polynomial regression (PR) is a stochastic model that has been widely used in forecasting in various fields. Stationary stochastic models play a very important role in forecasting. Generally, PR model parameter estimation methods have been developed for non-stationary PR models. This article aims to develop an algorithm to estimate the parameters of a stationary polynomial regression (SPR) model. The SPR model parameters are estimated using the Bayesian method. The Bayes estimator cannot be determined analytically because the posterior distribution for the SPR model parameters has a complex structure. The complexity of the posterior distribution is caused by the SPR model parameters which have a variable dimensional space. Therefore, this article uses the reversible jump MCMC algorithm which is suitable for estimating the parameters of variable-dimensional models. Applying the reversible jump MCMC algorithm to big data requires many iterations. To reduce the number of iterations, the reversible jump MCMC algorithm is combined with the Bootstrap algorithm via the resampling method. The performance of the Bootstrap-reversible jump MCMC algorithm is validated using 2 simulated data sets. These findings show that the Bootstrap-reversible jump MCMC algorithm can estimate the SPR model parameters well. These findings contribute to the development of SPR models and SPR model parameter estimation methods. In addition, these findings contribute to big data modeling. Further research can be done by replacing Gaussian noise in SPR with non-Gaussian noise.

KEYWORDS
Big Data, Bootstrap, Reversible Jump MCMC, Stationary Polynomial Regression

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Suparman , Eviana Hikamudin , Hery Suharna , Aryanti , In Hi Abdullah , Rina Heryani , "Forecasts with SPR Model Using Bootstrap-Reversible Jump MCMC," Mathematics and Statistics, Vol. 12, No. 2, pp. 167 - 174, 2024. DOI: 10.13189/ms.2024.120206.

(b). APA Format:
Suparman , Eviana Hikamudin , Hery Suharna , Aryanti , In Hi Abdullah , Rina Heryani (2024). Forecasts with SPR Model Using Bootstrap-Reversible Jump MCMC. Mathematics and Statistics, 12(2), 167 - 174. DOI: 10.13189/ms.2024.120206.