I have a monthly series of a moving average , and I want to reconstruct their original series from a simple moving average that I have. I happen to know the window of averaging.

Am I able to either reconstruct or estimate the original series from their moving average?

I have a monthly series of a moving average , and I want to reconstruct their original series from a simple moving average that I have. I happen to know the window of averaging.

Am I able to either reconstruct or estimate the original series from their moving average?

And in the case I don't have all the info to to fully reconstruct it, how about to estimate it?

I have a monthly series of a moving average , and I want to reconstruct their original series from a simple moving average that I have. I happen to know the window of averaging.

Is the process of moving average a lossy one or is information conserved?

Am I able to either reconstruct or estimate the original series from their moving average?

I have a monthly series of a moving average , and I want to reconstruct their original series from a simple moving average that I have. I happen to know the window of averaging.

Am I able to either reconstruct or estimate the original series from their moving average?