1. By assumption the Expected Value is zero everywhere ....thus one might wish to test this by implementing a CHOW TEST for constancy of parameters ....essentially computing means for two distinct groups i.e.observations before time period t and after t . One might find a shift in the mean thus signaling a possible change in parameters over time .
2. If there are no statistically significicanct difference between the before and after for ALL BREAK POINTS t then ...
3. Is the variance of the errors CONSTANT for all SUB-GROUPS and is the variability of the errors free of any dependence on the LEVEL of the series .
If all of these tests conclude in NON-SIGNIFICANCE and if the ACF/PACF of the Xt process indicates randomness ...then you might be good to go !
P.S. An example of time varying parameters is as follows
for observations 1 to t/2 y(t)=.9*y(t-1)+a(t)
t/2+1 to t y(t)=-.9*y(t-1) + a(t)
OVERALL the model is y(t)=0.*y(t-1) + a(t) BUT LOCALLY this is not true. THis is why you should ask your time series software vendor if they challenge the assertion that all t values should be used to identify/estimate/forecast . AFS's software ( http://www.autobox.com/freef.exe ) challenges this assertion often yielding the conclusion that there is TOO MUCH DATA or equivalently that the parameters have changed over time this violoating one of Karl's (Gauss ) premises.