Is it acceptable for a forecasting model to predict moving averaged version of the data? I'm working on a project in which I'm developing a precipitation forecasting model. 

When I try to predict the original data, the model (LSTM neural network) is not able to predict the peaks.

This is the predicted values for the original data:

 So, I decided to perform 

1) A differencing method in which I simply subtract values of the past from current values.

2) A moving average method on the resultant data from step 1.  

Then I try to predict this processed version of the data. 

Below is the predicted values for the smoothed data:


1) Is this kind of forecasting models acceptable among academicians? 

2) should I try just to predict the original data?

3) What probable usage can these types of predictive models (which forecasts smoothed version of the data) have?

4) Any suggestion on how to deal with this situation?
In estimation theory, the simplest way to estimate a random variable is to predict the average of its realizations. Very easy, very simple and very naive to be useful. 

Let me explain more: in your problem which is the weather, the correlation is very high between the data from the last several days and the next day, which makes your estimation a good one but in many problems, the corelation between the data from previous days and the next day is small ( the stock market). Another thing you need to keep in your mind which is the cost of doing a mistake, meaning, predicting the temperature to be the average of the last few days (75), if the actual temperature is 78, then the difference is 3 may be acceptable, in stocks, if the average from the last few days is 10 and the actual value is 10.5. This difference 0.5 may not be acceptable. 

What does mathematically this mean?
If the acceptable error in you estimation is &lt;&lt; than the variation within the data having an average based estimator is not acceptable.

Regarding the issue of transforming the data from one domain to another, it is okay if you a deterministic mapping function that can take you back to the original domain. We prefer to have one to one mapping