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

[hidden email] wrote:

> 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

>

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