marginal distribution wrt time of time series ?
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:
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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