The availability lag describes when the index is
available, not how it is used. Specifically the
fixing for, say, January, may only be available in April
but the index will always return the index value
applicable for January as its January fixing (independent
of the lag in availability).
Forecasting index values requires an inflation term structure. The inflation term structure (ITS) defines the usual lag (not the index). I.e. an ITS is always relatve to a base date that is earlier than its asof date. This must be so because indices are available only with a lag. However, the index availability lag only sets a minimum lag for the ITS. An ITS may be relative to an earlier date, e.g. an index may have a 2-month delay in publication but the inflation swaps may take as their base the index 3 months before.
Inflation indices do not have fixing calendars. An inflation index value is valid for every day (including weekends) of a calendar period. I.e. it uses the NullCalendar as its fixing calendar.
Forecasting index values using an inflation term structure uses the interpolation of the inflation term structure unless interpolation is set to false. In this case the extrapolated values are constant within each period taking the mid-period extrapolated value.
this method creates all the "fixings" for the relevant period of the index. E.g. for monthly indices it will put the same value in every calendar day in the month.