The Study of Continuous Hidden Markov Model and Its Application to The Price of Rice.

Abstract

Continuous hidden Markov model with discrete time (Elliot et al. 1995) is a model consists of the cause of event and observation process. This model assumes that the cause of event is a Markov chain in discrete time, observed indirectly. The observation process has continuous range and future observation is influenced by the cause of present event. Parameters of this model are transition probability matrices of the cause of event, vector and vector 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 7.0 functional programming computer algebra systems. The model is then applied to the price change of rice from February 2004 until May 2009. The estimated parameters are used to calculate the expectation value of rice price. As a result, this research convinces that the hidden Markov model can be applied to the price of rice.