Forecasting with ARMA models, from a filter point of view
ARMA divides the signal into two parts and that models the two parts.  

Financial time series are corrupted by different types of correlated and uncorrelated noises with definite functions that allow modeling and others more difficult as per having to use aproximations. In addition financial or economic times series may exhibit long memory processes (Black noise) or may have other long range dependencies or other non stationary issues. It is for this reason that besides the MA part it is hard to tell if a series is stochastic or deterministically chaotic or a mix between these.

The two terms of ARMA include an autoregresive term and a moving average term. The deterministic part of time series is modeled with ARIMA, ARFIMA etc family of models and the stockastic part using ARCH and GARCH family of models (usually volatility is modeled this way as a large portion of the stockastic part is white noise which can not be forecasted but its variance can).    

Diferenciation as you mention may eliminate some of the signal, however is necesary for regression in many cases as to make a time series weak sense stationary which is a requirement to have a meaningfull and valid regression. 

Signal to noise ratio is hard to guess for any unknonw noise+signal composition. However there are some ways to aproximate this by determining what noises affect your signal and what weights of noise correspond to each signal as well.

I would sugest from a signal procesing point to google / take a look at "financial / non stationary time series signal procesing" papers. There are many methods and ways as to extract information from a signal. 

I would sugest from a modeling point of view that you look at ARIMA or GARCH presentations from academia or papers from leading economic schools (LSE etc).

I will also sugest taking a look / google data preprocesing for regression (including the terms of unbalanced data set, stationarity, normality, linearity, aditivity and serial correlation, homocedasticity, spurious regression, cointegration, transformation of variables for financial time series).