Re: [Pen-l] FYI: Skidelsky on Keynes

[raghu <mraghu01@xxxxxxxxx>]

On Fri, Dec 19, 2008 at 8:07 AM, Julio Huato <juliohuato@xxxxxxxxx> wrote:
> raghu wrote:
>
>> I think the point is that a much weaker ergodicity assumption is
>> actually required than commonly assumed. For e.g., it may be necessary
>> to assume that herding and mob psychology will be pretty much the same
>> in future as in the past. But it is not necessary to assume that stock
>> price distributions are stationary (let alone ergodic).
>
> Actually, ergodic is weaker than stationary.  Ergodicity only requires
> that the time joint probability distribution be measure preserving.
> Stationarity requires that some traits of the time joint probability
> distribution be somewhat stable over time.


I have always found this very confusing: does not ergodicity imply
stationarity? Colloquially, in an ergodic system, time averages over a
single sample realization taken over a sufficiently long time
converges (in some mathematical sense e.g. mean-square) to the
ensemble average. But this only makes sense if the ensemble average is
constant in time, right?
-raghu.

-- 
"I used to do drugs. I still do drugs. But I used to, too." - Mitch Hedberg
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