Can white noise be removed using moving averages? In the book Time Series Analysis by R, the author mentions the use of moving average to smooth out the white noise.
Can moving averages be used to remove white noise or are there better methods?
 A: The role of the ARIMA structure is to convert colored noise to white noise. Smoothing out white noise would seem to be potentially creating colored noise. The concept of an oxymoron pops up in my head and I am not sure why.
A: Some thoughts on moving averages. [I think you edited your question to move from "MA model", part of the ARIMA (Box Jenkins) time series modeling family, to talking about "moving" or "running" averages, which is something different. Is this correct?]
First, per whuber's comments in IrishStat's answer, a literal moving average introduces correlation into your data. If you intend to do any analysis of your data after smoothing, you will be analyzing data with erroneous correlations added to it.
Second, a literal moving average is a binary operation: your samples pop into the window and out of the window 100%, which creates artifacts. These artifacts are a bit technical and have to do with the phase of your data -- engineers looking at signal waveforms care a lot about them. To avoid such artifacts, you should prefer a weighted moving average. (A moving average is a rectangular convolution, and you want something with smooth sides that go more gradually to zero effect.)
Third, a naive, centered moving average will use data from the future, which might be okay if you're just graphing something -- or it might not be -- but would be a big problem in any real analysis. 
Fourth, you need to ask yourself: why you want to remove or "smooth out" the noise? If all you want to do is make a less-busy plot, this may be okay, but if you intend to smooth your data and then analyze it, you are modifying your data in multiple ways that will distort any analysis: introducing spurious correlations, changing phases, fooling analysis techniques into being over-confident of their results, etc.
If you state your analytical goal -- rather than just wanting to eliminate noise -- you'll get a better answer.
