Why use differencing and Box-Cox in time series? Why use Differencing and Box-Cox transformation in a time series? From what I read the usefulness of the procedures are


*

*Differencing: Making a time series stationary and stabilize the mean

*Box-Cox: stabilize the variance
Is there anything else behind it?
I know that there is some useful properties in a Stationary Process, but why is so important have it? 
 A: The Box-Cox transformation is a family of power transformations indexed by a parameter lambda.  Whenever you use it the parameter needs to be estimated from the data.  In time series the process could have a non-constant variance. If the variance changes with time, the process is nonstationary.  It is often desirable to transform a time series to make it stationary.  Sometimes after applying Box-Cox with a particular value of lambda the process may look stationary. It is sometimes possible that even if after applying the Box-Cox transformation the series does not appear to be stationary, diagnostics from ARIMA modeling can then be used to decide if differencing or seasonal differencing might be useful to remove polynomial trends or seasonal trends respectively.  After that, the result might be an ARMA model that is stationary. If diagnostics confirm the orders p and q for the ARMA model, the AR and MA parameters can then be estimated.
Regarding other possible uses of Box-Cox in the case of a series of iid random variables that do not appear to be normally distributed there may be a particular value of lambda that makes the data look approximately normal.
Presumably, this could be applied in regression or time series to the error term.
