# References to time series feature stability with varying series lengths

Firstly I'd like to note that according to a discussion in meta this question is indeed on topic.

I have trouble finding relevant research related to time series analysis. I'm interested in how features calculated from series behave as the series grow or shrink in length. Is there any literature related to such analysis?

As a concrete example we could analyse the electricity consumption of some household. I would argue that using a mean would stabilise rather quickly while a difference of the last two values would not stay as put. They are simple features, but more interesting ones, like distribution qualities or other statistics could be used just as well.

So far, using Google Scholar, I've found no such results with searches like time series "feature dynamics" or time series "feature stability". The most relevant works like 1 and 2 deal with the stability of features in some related domains, but never examine the stability as a function of series length. 3 seems more related, but unfortunately I have no access to it. The quotes around search terms are for matching words strictly together. Without them all articles were about time series dynamics, as measured by some features, which I'm not interested in.

Remembering specific relevant articles is perhaps asking too much, but would you have advice for searching for this kind of literature? It seems unlikely that it doesn't exist at all.

Let us calculate a feature $$f$$ from data $$x(t)$$ with varying history lengths $$h$$. The resulting series $$f(x(t), h)$$ is in itself a time series. To examine the stability of $$f(h)$$ we can use the same techniques that could be applied to $$x(t)$$.