Predicting ATM Withdrawal using Modified Triple Exponential Smoothing
- 1. Predicting ATM Withdrawal Using Double Exponential Smoothing Evellyn Verity Mesak, Muhammad Husnurridlo Summary The following report describe methodology and exploratory process in prediction of ATM cash withdrawal. The data is compiled and provided by FinHacks 2018. We think the biggest challenge of this project is finding a pattern that can be applied for 10.626 ATM with various withdrawal behavior. Taking several ATMs’ behavioral data as samples, we concluded that generally, the withdrawal following two big pattern: the weekly cycle and the monthly cycle. With that in mind, the solution we propose is establishing a level and a unique index everyday based on the weekly and monthly cycle. For example, an ATM has 100 Mil IDR withdrawal (level). The withdrawal on Thursday is 60% of level, and the withdrawals on 29th every month is 150% of level. With those numbers known, we can predict the withdrawal for Thursday March 29th . WithdrawalMar29 = 100 Mil * 60% *150% = 90 Mil. Now, based on this idea, all we need to do is find the suitable level for each ATM and the index for every day of the week and every date of the month. The Dataset The analysis and modelling we create is based on 881.816 daily withdrawal data of 10.626 ATM. Most ATMs have observation from January 1st 2018 to March 24th 2018, except ATM no K10301, which only has observation from March 19th 2018 to March 24th 2018. We use column “no atm”, “date”, and “withdrawals” to build the model. Feature Engineering a. Weekly Seasonal Index The goal in this step is to find suitable index for every day of the week. The method is pretty simple. For each ATM, we calculate average withdrawal for each week, so we have 12 weekly average for each week. After that, we calculate index for each day by taking the withdrawal that day divided by weekly mean. Then, we take the average weekly index of the same day and then average it across 12 weeks to find day index. Back to the example in the summary, this is how we get the number 60% for Thursday. The difficulty we faced in building this feature is there are some ATMs that has consecutives zero withdrawals for more than 7 days. This creates error when we create day index due to division by zero. To deal with this, we replace the zero weekly average with one.
- 2. b. Monthly Seasonal Index The goal in this step is to find suitable index for every date of the month. By doing almost the same step for the weekly seasonal index, this can be done. For each ATM, we calculate the average withdrawal for each month, so we have average withdrawal for January, February, and partial average of March. After that, we calculate index for each date by taking the withdrawal that day divided by monthly mean. Then, we take the average monthly index of the same date and then average it across 3 months to find date index. Back to the example in the summary, this is how we get the number 150% for 29th . c. Level This is where the double exponential smoothing plays a role. The double exponential formula we use is as follow: 𝑎 𝑡+1 = 𝛼 ∗ 𝑌𝑡 𝑆𝑡 + (1 − 𝛼) ∗ (𝑎 𝑡 + 𝑏𝑡) 𝑏𝑡+1 = 𝛽 ∗ (𝑎 𝑡+1 − 𝑎 𝑡) + (1 − 𝛽) ∗ 𝑏𝑡 𝑦𝑡+1 = (𝑎 𝑡+1 + 𝑏𝑡+1) ∗ 𝑆 𝑚𝑜𝑛𝑡ℎ ∗ 𝑆 𝑤𝑒𝑒𝑘 The 𝛼 and 𝛽 parameter represent how fast we take new information from latest observation. We look for the value that minimize the error between prediction and actual observation. We use spiral optimization method to optimize the parameter values. Prediction After we got the latest level for each ATM that is the level at March 24th 2018, we use that level to predict one week forward for March 25th until March 31st using the month and week seasonality that we have calculated before. The equation become: 𝑦𝑖 = (𝛼 + 𝛽) ∗ 𝑥𝑖 where 𝑦𝑖 is prediction for ATM withdrawal, 𝛼 and 𝛽 are level and trend respectively, and 𝑥𝑖 is actual ATM withdrawal with error, 𝑒𝑖 is defined as 𝑒𝑖 = | 𝑦𝑖 − 𝑥𝑖 𝑥𝑖 | We use spiral optimization method and we set minimizing error as objective function. To test if the model is overfitted, we train the model using the data up until 18 March 2018 and use 19-24 March as “testing” data. By using this, we have expected accuracy of 66% error fall under 25%. Following is some of the result of our prediction