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marginal distribution wrt time of time series ?

2 messages · cmdrnorton@poczta.onet.pl, Spencer Graves

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
4 days later
Spencer Graves
# 
I don't have a citation, but I think as long as the process is 
stationary and not completely deterministic, the concept of a marginal 
distribution is well defined and data from such a process will 
eventially converge to that distribution.  Of course, as the level of 
dependence increases, the number of observations to obtain reasonable 
convergence will increase.

	  Standard goodness of fit test will NOT work with dependent series, 
but that's another issue.

	  Perhaps someone else will provide further details.

	  hope this helps.
	  spencer graves
cmdrnorton at poczta.onet.pl wrote: