Given this time series data:
tbl <- tibble(month = c('jan', 'feb', 'march', 'april'), mob1 = c(20, 24, 27, 25), mob2 = c(15, 17, 19, NA), mob3 = c(11, 12, NA, NA), mob4 = c(8, NA, NA, NA))
I would like to predict the values for each of the NA's. the forecast for each month should be based upon the available data for that specific month, and also based upon the patterns present in the other months. Is there an analytical technique that I could use to make these predictions? In reality my data is much larger than the example given.
EDIT: DESCRIPTION OF THE REAL DATA
The real data consists of 39 months of data (so 39 columns), for each month from mid 2013 to the present (55 + rows). The dataset is comprised of loan repayment data. Specifically, the percentage of a loan that gets repaid every month until the whole loan is repaid. Cases, (rows) consist of sum of the cost of all the loans that were dispersed in that month., then columns mob1...mob39 consist of the percentage of the amount dispersed in that month that gets repaid. For example, the percentage of all the loans that were dispersed in January 2014 could be 3.3% after one month, then 3.1% after two months, and so on until the end of the loan term, and in theory the percentages all add up to 100%. In reality the percentage that gets repaid each month gradually decreases, starting from about 3.5% in month1 to about 1.3% in month39 (on average) so there is no seasonality to the data data, but rather each case has a gradually decreasing percent of the total loan amount across the 39months.
My internet search shows the ARIMA model to be something I could possibly use (at least that is what keeps popping up!), however, my data doesn't have seasonality to it and thus ARIMA might be an overly complicated solution, and from what I understand the ARIMA model doesn't take advantage of the patterns present in different cases in order to predict the NA's in said case. What I mean by this is, for example, the I would like to forecast the NA months for February, using not only the existing data for February, but also the data from the preceding January time series, as both show similar patterns. I'm not sure if that is common practice but to be it seems intuitive to do so.
Any help that can be given would be greatly appreciated!