[R] marginal distribution wrt time of time series ?

[cmdrnorton@poczta.onet.pl]

Dear all,

In many papers regarding time series analysis 
of acquired data, the authors analyze 'marginal 
distribution' (i.e. marginal with respect to time) 
of their data by for example checking 
'cdf heavy tail' hypothesis. 

For i.i.d data this is ok, but what if samples are 
correlated, nonstationary etc.? 

Are there limit theorems which for example allow 
us to claim that for weak dependent, stationary 
and ergodic time series such a 'marginal distribution 
w.r. to time' converges to marginal distribution 
of random variable x_t , defined on basis of joint 
distribution for (x_1,…,x_T) ? 

What if the correlation is strong (say stationary 
and ergodic FARIMA model) ? 

Many thanks for your input

Norton