Kajian Model Hidden Markov Kontinu dan Aplikasinya pada Harga Gabah Kering Panen

Abstract

Continuous hidden Markov model (Elliot et al. 1995) is a model that consists of the cause of event and observations process. This model assumes that the cause of event is a Markov chain which is not observed directly, and the observations have continuous-range. Parameters of this model are transition probabilities, expectation and variance of observation process. They are estimated by using the maximum likelihood method and expectation maximization algorithm that involves the change of measure. Model parameters were estimated by using Mathematica 6.0 a functional program based computer algebra systems. The model was applied on price change of harvest dry rice in 2000 until 2007. The estimated parameters were used to calculate the expectation value of harvest dry rice price. The result of this study showed that the continuous hidden Markov model could be applied on harvest dry rice price.

Proses Markov merupakan proses stokastik dengan sifat bahwa perilaku stokastik di masa yang akan datang hanya bergantung pada perilaku masa sekarang. Setiap kejadian berkaitan erat dengan penyebab kejadian tersebut. Jika penyebab kejadian tersebut tidak diamati secara langsung dan membentuk rantai Markov maka pasangan kejadian dan penyebabnya dapat dimodelkan dengan model hidden Markov (HMM). Misalkan X = {Xk;k e N}adalah rantai Markov yang bersifat homogen dan tidak diamati secara langsung, sedangkan Y = {~;k e N} adalah proses observasinya. Pasangan {(Xk'~)} merupakan model hidden Markov