In time series analysis we often deal with just one time series, so many time series analysis methods have been developed based on stationarity (see this question) .
However sometimes we can have sample of time series related to the same phenomenon.
To make an example, we could have many time series representing, each, the number of news media articles published about a particular event, say political elections, over one month. In this case we could have a data set comprising many time series of number of news media articles published on different elections disputed over time, maybe also across countries, and we could hypothesize that there is a common data generating process behind them.
Which kind of methods are available to analyze this kind of data set? Could you give me some hints about the keyword I have to search for to find something about this? If you want, I’d also appreciate some practical examples of approach to the analysis of data sets like the one in the example or a similar one (it is not a real case).