marginal distribution wrt time of time series ?

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marginal distribution wrt time of time series ?

cmdrnorton
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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Re: marginal distribution wrt time of time series ?

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

[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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

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