Pemodelan Nilai Tukar Rupiah terhadap Dollar Amerika Menggunakan Deret Waktu Hidden Markov Empat Waktu Sebelumnya

Abstract

The exchange rate of Rupiah to US Dollar fluctuates according to time in a long period. An existing exchange rate might happen again in the future. Assume that the causes of the fluctuation are not observed directly and form a Markov chain, then the exchange rate of Rupiah to US Dollar can be modeled by the hidden Markov time series. In this research, the model used to describe the exchange rate of Rupiah to US Dollar is the four previous time in hidden Markov time series. This model assumes that the exchange rate of Rupiah to US Dollar depends on Markov chain explained by the cause of occurence and the four previous exchange rates of Rupiah to US Dollar. The model parameter is estimated by using the maximum likelihood method, while the estimation itself is calculated using the expectation maximization algorithm, which is implemented using Mathematica. After estimating the parameter, the exchange rate of Rupiah to US Dollar are calculated. The results are as follows. The symmetric mean absolute percentage error (SMAPE) is 2,1%, the maximum absolute error is 19,16%, the minimum absolute error is 0,0036%, and only 1,95% of the whole absolute percentage error that is bigger than 10%. These results show that the four previous time in hidden Markov time series can describe the exchange rate of Rupiah to US Dollar very well.