I am looking for information on (formal) algebraic systems that can be used to transform time-series - in either a practical or academic context.
I hope that there exists (at least one) small, expressive, set of operators - ranging over (finite) time-series. I want to compare and contrast different systems with respect to algebraic completeness, and brevity of representation, of common time-series transformations in various domains.
I realise this question is broad - but hope it is not too vague for datascience.stackexchange. I welcome any pointers to relevant literature for specific scenarios, or the general subject.
Edit... (Attempt to better explain what I meant by an algebraic system...)
I was thinking about "abstract algebras" as discussed in Wikipedia:
Boolean Algebras are (very simple) algebras that range over Boolean values. A simple example of such an algebra would consist the values True and False and the operations AND, OR and NOT. One might argue this algebra is 'complete' as, from these two constants (free-variables) and three basic operations, arbitrary boolean functions can be constructed/described.
I am interested to discover algebras where the values are (time-domain) time-series. I'd like it to be possible to construct "arbitrary" functions, that map time-series to time-series, from a few operations which, individually, map time-series to time-series. I am open to liberal interpretations of "arbitrary". I would be especially interested in examples of these algebras where the operations consist 'higher-order functions' - where such operations have been developed for a specific domain.