Pemodelan Jumlah Penumpang Kereta Api di Sumatera Menggunakan First-order dan Higher-order Markov Chain

Abstract

First-order Markov chain model is a Markov chain model that depends only on the last state, while higher-order Markov chain model is a Markov chain model that relies on past some states. The purposes of this research are to study the first-order and higher-order Markov chain models and their parameter estimation and to apply these models for modeling the number of train passengers in Sumatera. The data used in this research are data of the number of train passengers issued by Statistics Indonesia starting from January 2007 until December 2013. Numerical calculation is performed using the softwares Mathematica 9.0 and Microsoft Excel 2010. For 4-state and 5-state models, we obtain the accuracy of model of 51.81%. Based on these results, we can conclude that first-order and higher-order Markov chain models are not suitable models for the number of train passengers in Sumatra.