Time series notation

Question

I'm developing formal software requirements specifications for processing time series data and thus need to mathematically describe time series and operations on time series. Is there establish notation for doing this? There seems to be some variability in how time series are described and even referred to (e.g., sets, sequences, series). Is it appropriate to borrow set notation? For example, would |N| be appropriate for describing the number of elements in a time series, in this case defined by the sequence N. If I want to append a data point to the start of a time series or join two time series what notation would be appropriate? If time series were sets this would be the union operation (for which there is a standard notation), but what notation is best in the case of time series.