Implementation of Markov Chain on MSME Data for QRIS Users in Medan City

QRIS (Quick Response Indonesian Standard) is a non-cash payment system innovation initiated by Bank Indonesia in collaboration with the Indonesian Payment System Association. This is one response to the era of digitalization and industry 4.0. Since January 2020, Bank Indonesia has required ( implemented) QRIS for non-cash payments, especially for micro, small and medium enterprises (SMEs), because it is a sector that contributes to Gross Domestic Product. Therefore, this study is intended to predict the number of SMEs using QRIS in Medan in the future based on the Markov Chain method. The data used is the number of MSMEs that use QRIS as a cashless payment in Medan City from Bank Indonesia North Sumatra in December 2019 to June 2022. The results show that there is a balance in October 2022 with a 52.2% chance percentage with declining conditions; 30.4% with an increasing condition, and 8.7% with a strongly increasing and decreasing condition. This good accuracy is checked with Mean Absolute Percentage Error (MAPE).

QRIS (Quick Response Indonesian Standard) is a non-cash payment system innovation initiated by Bank Indonesia in collaboration with the Indonesian Payment System Association. This is one response to the era of digitalization and industry 4.0. Since January 2020, Bank Indonesia has required ( implemented) QRIS for non-cash payments, especially for micro, small and medium enterprises (SMEs), because it is a sector that contributes to Gross Domestic Product. Therefore, this study is intended to predict the number of SMEs using QRIS in Medan in the future based on the Markov Chain method. The data used is the number of MSMEs that use QRIS as a cashless payment in Medan City from Bank Indonesia North Sumatra in December 2019 to June 2022. The results show that there is a balance in October 2022 with a 52.2% chance percentage with declining conditions; 30.4% with an increasing condition, and 8.7% with a strongly increasing and decreasing condition. This good accuracy is checked with Mean Absolute Percentage Error (MAPE).

INTRODUCTION
In line with economic developments and changes, the use of digital technology or known as economic digitization has also increased. The development of the digital economy that occurred in Indonesia in October 2019 had reached USD 40 billion or IDR 556.6 trillion. growth in the digital economy sector in Indonesia is much helped by e-commerce which is growing very fast [1]. The impact resulting from the acceleration of economic digitization will greatly affect the economic welfare of the community.
Based on research data conducted by [1] it is known that the increase in Indonesia's digital economic growth is strongly influenced by a lot of e-commerce in Indonesia. The situation prompted Bank Indonesia to improve the payment system with the launch of the Quick Response Code Indonesia Standard (QRIS) [2]. QRIS is the unification of various QR codes from various Payment System Service Providers (PJSP) using a QR Code , launched on August 17, 2019 QRIS is a new program initiated by Bank Indonesia in collaboration with the Indonesian Payment System Association (ASPI) as a form of digital payment transformation. In the QRIS program as of January 1, 2020, it is mandatory for all merchants , namely product/service sellers who accept payments via e-money [2].
The first application of QRIS is for MSME traders [3]. The number of MSMEs in 2021 will reach 64.2 million with a contribution to GDP (Gross Domestic Product) of 61.07% or worth 8,573.89 trillion rupiah, the data provides a statement [4] where MSMEs have great potential in providing a role for the economy . With the collaboration between MSMEs and electronic money providers, it will improve finances, including advancing the Indonesian economy [3]. For that, we need to see to what extent this QRIS is realized through data on MSMEs that have used QRIS in their transactions. The more MSMEs that use QRIS, the objectives of standardizing payments by Bank Indonesia and increasing financial inclusion in Indonesia can be realized.
The data of MSME users who use QRIS in their transactions in the future is related to the extent to which QRIS data users are today. Because based on the QRIS guidelines, a QRIS user only has 1 QRIS account, in other words, there are no double-registered accounts. With the new habit of making non-cash transactions by customers, the use of QRIS has increased. So they don't want economic actors, one of which is MSMEs, to provide efficient non-cash payments, namely QRIS. This condition meets the requirements of the Markovian Property , which states that the conditional probability of a future event depends only on the present state and does not depend on the previous state. Markov chain was developed by a Russian expert named AA Markov in 1896. In the analysis of Markov chain the resulting probabilistic information that can be used in decision making. This technique can be used to predict future time changes in dynamic variables on the basis of changes in these variables in the past [5].
In this study, it will be seen how the implementation of QRIS on MSMEs in the city of Medan will be made where predictions will be made to obtain probabilistic information for each period based on an analysis of factual data obtained from Bank Indonesia. The data used to fulfill the stochastic process, namely the data changes over time. In accordance with Markov's nature, current conditions contain relevant information to predict future conditions in a probabilistic sense, and past conditions only affect current conditions. Where in probabilistic, if the probability value of the event is close to 1, then the probability of the event occurring in the future will be even greater [7].
This study aims to see the extent to which the QRIS policy has been implemented through data on MSMEs using QRIS in the city of Medan through predictions of MSME data using QRIS users in Medan in the future with the hope that the results can be used by economic actors and other government agencies to optimize efforts to digitize the economy through non-cash payment transactions, namely QRIS. This is in line with the efforts made by Bank Indonesia to respond to challenges in the digital era and industry 4.0, namely the Indonesian Payment System Blueprint (BSPI) 2025 [8].

Research data
The data used in this study is data on the increase in the number of MSMEs in the city of Medan using QRIS for the period December 2019-June 2022. Data obtained from the Bank Indonesia Representative Office, North Sumatra.
Research Stages R programming language assistance . Some of the steps taken in implementing Markov Chain on MSME data for QRIS Users in Medan City are as follows: The n-step Transition Probability Matrix is obtained by multiplication between matrices, where () ml p + is the n-step transition probability matrix, 6. Predict the probability of the data in the future until it reaches a steady state.
Obtained by the following equation , Where ( 1) Qn+ is the probability prediction of the data, T P is the transition matrix with the power of the forecast period and () qn is the condition of the data at time n. Fixed-State Probability ( Steady-State Probability ) can change with the opportunities in every situation will not pass time. This shows that after the process has been running for several periods, the opportunity value will be stable in the long term.

Test the accuracy of predictive data. Mean Absolute Percentage Error (MAPE)
is the average value of the absolute difference that exists between the predicted value and the realized value stated as a percentage of realization, with the formula [10]: Where n is the sample size , i A is the actual data value and i F is the forecast data value.
8. Conclusions are drawn by presenting data predictions until they reach a steady state supported by the accuracy test of the research.

Research data
Data obtained from Bank Indonesia is an accumulation of the number of MSMEs consisting of the Medium, Small and Micro categories from period to period. The policy on using QRIS for MSMEs has been set since December 2019 and implemented nationally as of January 2020, therefore in this study the data used for the period December 2019 to June 2022. However, in this case, the data used to predict is the data for the period December 2019 to December 2021. , and the data for the period January 2022 to June 2022 will be used as actual data in the process of testing the accuracy of the predictions.

Transition Opportunity Matrix
The following is the data changes or songs from the QRIS MSME data in the city of Medan: , , , P P P P P = where 1 P = increases 2 P drastically, 3 P = decreases, 4 P = decreases drastically. The frequency of the QRIS MSME Data can be seen in the following matrix Or it can be presented as follows, The probability at the equilibrium state level or steady probability is the probability that it has reached equilibrium, so it will not change the changes that occur or changes in the stages that occur. With the country 's potential This step will provide important information about the n steady state probability value of a system. Based on the table above, it can be seen that each vector represents the MSME QRIS value in the city of Medan above which it converges to a fixed vector. MSME data QRIS users in Medan City experienced steady state conditions in the 10th period. So if a simulation is carried out for the 11th period and so on, the chances will be the same as the 10th period.
Then it is known that, 1. The Opportunity for the Medan City QRIS MSME Value to be in a Drastic Increase is 8.7% 2. The opportunity for the Medan city QRIS value of SMEs to be in a state of increasing is 30.4% 3. Opportunity for the Medan City QRIS MSME Value to be in a Downturn is 52.2% 4. The Opportunity for the Medan City QRIS MSME Value to be in a Drastic Drop is 8.7%

Prediction Accuracy Test
In doing a forecast, the accuracy of the forecast is very important so that the forecast can be used in everyday life. To test the accuracy of predictions in this study, the MAPE ( Mean Absolute Percentage Error) test was used . it can be seen that in December there were 17,955 MSMEs in the city of Medan that used QRIS. It is assumed that the Prediction Data is at a predetermined interval at the beginning of the study by maintaining the position of the data position. By using equation (5) it is obtained, Based on the results of the prediction accuracy test using the MAPE test, the prediction accuracy value is 19.38%. According to the rules of the MAPE test in Table 4, the accuracy of the predictions made in the study is in the Good category.

CONCLUSION
The results showed that predictions from the data on the number of QRIS users ( Quick Response Code Indonesian Standard) by MSMEs (Micro, Small and Medium Enterprises) in the city of Medan changed each period, predictions for each period were obtained by multiplying the transition matrix for the forecast period with the conditions data in time to n . Based on steady state predictions , after the 10th period onwards the probability of the data will be in a stable condition where the number of QRIS user data by MSMEs in the city of Medan will be in a "Down" condition with a 52.2% chance. The accuracy of the data prediction using the MAPE test ( Mean Absolute Percentage Error) is in the good category with a MAPE value of 19.38%.