Definition talk:Time Series

The definitions here are very informal and use non-standard language to describe mathematically what a time series is.

What would you regard "standard language" to be? --prime mover (talk) 16:49, 9 August 2022 (UTC)

The wikipedia page for stochastic processes and time series are both exact and contain informal definitions. A stochastic process is a collection of random variables with a joint probability measure satisfying a consistency property. A time series is a realization of a stochastic process. What you call "timestamps" refers to the index set of the random variables, and it does necessarily need to be a contiguous subset of the natural numbers, as is the case with solutions to stochastic differential equations. If you want a textbool, I suggest Brockwell and Davis 1991. While the full measure theoretic treatment is serious overkill for almost all practical applications, it is important in the sense that there is a clear philosophical model that we believe we are sampling.