Obviously this is an advanced(ish) topic in statistics, so you can explain like I’m 15.
In: Mathematics
Like… are you looking for an explanation of the proof? Because I have no idea how to event begin explaining Hilbert spaces to a 15 year old, even one that is immensely mathematically precocious.
Are you having problems with something in particular? At a high level it just means that if you have a stationary time series, it is always possible to decompose the series into a pair consisting of deterministic time series (one which, given an infinite number of past data points, provides perfect predictive power – i.e. what you’re trying to isolate) and a stochastic time series (one where each data point represents a random result of a process at that instant – i.e. noise).
The simplest explanation I know if is the short primer given in this text on handling time-series in R.
https://smac-group.github.io/ts/introtimeseries.html#the-wold-decomposition
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