Application of Fuzzy Time Series-Markov Chain Method in Forecasting Data of Exchange Rate Riyal-Rupiah

Currency rates are one of the important indicators in the context of an economics country. The value of a country’s currency always increases and decreases in value against another country’s currency at any time. In this research, we make a model of dynamical currency rates data among Riyals and Rupiah. The data are obtained from the official website of Bank Indonesia. The aim research is to predict the currency rate between Riyal to Rupiah in the future time with the Markov Chain Fuzzy-Time Series method. The results of this research are data processing in the form of error value of the forecast used AFER and MEA methods. Those are 0.827% and Rp32.96 rupiahs respectively. The forecast value for the next 10 days are Rp3,779; p3,774; Rp.3,774; Rp3,779; Rp3,764; Rp3,760; Rp3,763; Rp3,797; Rp3,777 and Rp3,784.


Introduction
One important indicator in a country's economy is the exchange rate [1]. Currency exchange rates have a broad implications in both domestic and international economic context. This is because remembering that almost all countries in the world carry out international interactions with other countries [2]. There are various kinds of countries in the world that conduct international relationship with other countries. A trade collaboration, foreign investment, tourism are the examples of international relationship kinds. Indonesia and Saudi Arabia kingdom has cooperation in manage Hajj and Umroh. Indonesia is a country with the most Muslim population in the world.
Every year more than 200,000 of moslem Indonesians go on pilgrimage for Hajj to Holy Land in Mecca, Saudi Arabia. Every year also more than one million moslem Indonesians go on pilgrimage for Umroh to there. Based on statistics released international Hajj by Saudi Arabia in year 2018, recorded as many as 1,049,496 pilgrims in holy land comes from Asia for Hajj. There are 203 351 of them are moslem from Indonesia. While the number of pilgrims for Umroh from Indonesia in 2018 reached 1.1 million people [3]. The moslem Indonesian who pilgrims for Hajj or Umroh certainly need Saudi Arabia currency to make transactions in the holy land. Saudi Arabia Riyal (SAR) is the currency of Saudi Arabia Kingdom [4].
The value of a country's currency always increases and decreases in value against another country's currency at any time. The increase and decrease of value of these currencies occurs because of several factors. One reason is because of the law of supply and demand on SAR currency transaction [5]. In the Hajj season, the demand for Riyal currency in Indonesia has increased from the previous months. For example the value of Riyal currency in the day that is not Hajj season only around Rp 3,870/ Riyal then it will be increase to Rp 4,700/ Riyal when Hajj season The number of demand has a significant impact on the increase or decrease in currency values. The increasing or decreasing of it is referred to fluctuations of exchange rate. We can see how fluctuations of currency movements. Here is a data plot of exchange rate between one Riyals to Rupiah for six months in the end of year 2018. Based on Figure 1, we can be seen that the value of SAR currency has increased and decreased in value IDR. From the graph, it is known that the highest value in that period was on 11 October 2018 and the lowest value on 3 December 2018. In year 2018, the peak of the hajj season or better known as Eid Al-Adha occurred on August 22, 2018. The graph shows that in the hajj season and the period before the peak of the hajj season, currency tend to increase. The increase occurred from the beginning of August 2018 until the end of the pilgrimage season. At the beginning of the month of November when the pilgrimage season ended Riyal tends to go down.
We can find out the price of a currency in the future time use a forecasting method. The forecasting is an estimate of something that has not yet happened [6]. The forecasting is needed in the decision making process. The field of economics forecasting can be used to monitor the movement of the exchange rate of the coming period. So that the forecasting will provide a basis or reference for economists in making a planning and decision making to increase profits and prevent losses [2]. One method that can be used for forecasting is a model Fuzzy Time Series-Markov Chain. This method is triggered first by Tsaur in the year 2012. In Tsaur research combines methods Fuzzy Time Series with Markov Chain (FTSMC). This is done to obtain the greatest probability using transition probability matrix which is used on the Markov Chain. In his research of probability methods Fuzzy Time Series Markov Chain (FTSMC) gives an accuracy good enough. Forecasting procedures using the Markov Chain-Fuzzy Time Series method has several stages defined according to [7] and described in [8].

Method
This study includes applied research with the type of data used is secondary data obtained from the Indonesian official website, namely https://bi.go.id [9]. In this study, the data used Riyal Currency Exchange Rate data against the daily Rupiah with a period of 6 months. The stages to be carried out in this study are as follows:  Input data of exchange rate of Riyal-Rupiah

Results and Discussion
Every day the value of the exchange currency in any country has always experienced an increase or a decrease in the value of the currency to other countries. The increasing and decreasing of currency value also occurs between Saudi Arabia (SAR) and Indonesia (IDR). In [8] the transition probability matrix from data has been obtained by the Markov Chain-Fuzzy Time Series method. Following are the exchange data model: From the model obtained, then determine the initial forecasting results from Riyal data against Rupiah. The calculation for the initial prediction starts on the second data from the historical data on August 24, 2018. For example from the calculation of the initial forecast value for the data on September 4, 2018 (9th data) and September 26, 2018 (24th data ) where in the data the state transitions from A5 to A6 and A6 to A5 with FLRG from the data is one to many . The calculation is as follows: The next step of this method is to determine the adjustment value by using the equation and the rules that apply at this stage contained in [8]. As an example of data calculation for September 3, 2018, the FLR is known as A5 to A6, the calculation is as follows: ( , = .
For results value adjustments show in Table 2 . The final stage of this method is to determine the value of the Final forecasting, where the initial forecasting results have been adjusted or added to the existing adjustment values using equations and rules that apply to this hold . An example of a calculation is as follows:  All proceeds forecasting the end of the value data exchange of Riyal-Rupiah are obtained by the equality and the applicable rules and be viewed in Table 2. To see the comparison of Actual EXCHANGE data with the Model data from forecasting can be visualized into the graph as follows: