How to save state when extending UIComponentBase

Question

I'm creating a composite component that will wrap a datatable to implement very simple paging. I need to save state (the current page number) between ajax requests.

I tried creating fields in my FacesComponent, but I discovered they are wiped out during the JSF lifecycle:

@FacesComponent(value = "bfTableComponent")
public class BFTableComponent extends UIComponentBase implements NamingContainer {

    private int currentPageNumber;
    ...

I can't seems to find a concise guide to doing this anywhere! How would one save state between requests when creating a composite component?