Talk:Wold's theorem

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Clarifications sought

It seems to me that t must be defined as indexing time at a point long after the possible start of observations so that j can range to infinity back from t. Also, it is not clear to me whether all the b_j remain the same or change as t increments. I understand, tentatively, that b₁ becomes b₂, and similarly for all j, when t becomes t+1.Ajrc (talk) 15:57, 13 October 2010 (UTC)[reply]

See comment below...this applies to a stochastic process, so there is no "start of observation". The b_j's are fixed and possibly stretch back infinitely far. 104.187.53.82 (talk) 00:11, 13 July 2023 (UTC)[reply]

Fundamental misconception within the article about the difference of time series and stochastic processes

In the intro section talks about "covariance-stationary time series " which do not exist. It does not make sense to speak of stationarity of a time series. That is the property of a possible underlying process generating the time series, but not of the time series itself, which is just one path of the stochastic process. In the follow up explanation of the fundamental decomposition equation the text suddenly jumps back to stochastic processes in contrast to time series. This should be changed to achieve consistency (and correctness). — Preceding unsigned comment added by 183.89.188.102 (talk) 11:18, 5 January 2019 (UTC)[reply]

Informal Statement

I would like to see a more formal statement of the theorem. The phrase "covariance-stationary" points to another article that doesn't mention such a thing, for example. What are the minimal requirements on the stochastic process required to apply the theorem? — Preceding unsigned comment added by 104.187.53.82 (talk) 00:14, 13 July 2023 (UTC)[reply]