Time series forecasting when historical data are provided in batches I am working on a forecasting problem with hourly time-series data. Working on historical data I have deployed several models which take as input previous values e.g at time t-1,t-2,t-3... etc and forecast value at time t or t,t+1,t+2. So for every model I have tried so far it is necessary to provide as input the previous actual values. 
My problem is that in a real case scenario, I have no knowledge of previous hourly data. If it helps, I get the actual values in batches every 4 months. So if I want to forecast value at time t or t+1, I would need values at times t-1,t-2,t-3, etc. which I don't have. The actual values I have are 3 or 4 months ago. So my model has no input.
So far I have tried recursive strategies i.e. use previous forecasted values as input but I get bad results because 3 or 4 months is a long period. Ideally, I would like to forecast 24 values (1-day) ahead. So my question is what strategy I could follow to solve that problem.
I have read about limited historical data problems, but that is not exactly my case, because I actually have historical data but I get that in batches every 3-4 months.
Any help is greatly appreciated
 A: There is little else you can do but do a long-range forecast based on the data you have. If your last historical data is from four months ago and you need an hourly forecast for tomorrow, you will need to calculate a four-months-plus-one-day hourly forecast. Yes, this will probably be very inaccurate.
Don't invest your time and efforts in looking for fancy models that can magically solve this problem. (If such an approach existed, it would be used for long-range forecasts in the first place.) Rather, try to get more recent data.
A: One method that could be used in a situation like this - although one would need to take a great deal of caution in doing so - is linear interpolation.
For argument's sake, let's suppose that you are trying to forecast hourly temperature values. At 12:00am, the outside temperature is 7°C, and rises to 15°C by 3:00pm that day.
Given that 8/9 = 0.8889, one could conclude that the temperature is rising by 0.8889°C per hour within that time period, and formulate dummy data that "fills in the blanks" of the time series, so to speak.
However, as I mentioned, such a method requires a great degree of care and knowledge regarding the proper structure of your data. One obvious disadvantage is that this method does not account for outliers, e.g. the temperature could drop to 2°C at 6:00am before rising - the data will never follow a perfect linear pattern.
Your best bet is to try to obtain real data wherever it is possible. Simulating data in this manner could be another option, but it is not ideal and you need to take a lot of care in doing so.
