Autocorrelation with (LOTS) of missing data.

I've got a time series 807793 bins long, with missing data in all but
48945 of those bins. Only 7392 of those bins have a non-zero event
count. Those bins have a total count of about 1 million events, which
tells you that events are highly clustered, at least at the time scale
of the bin size (5 minutes).

I want to use autocorrelation analysis to investigate the clustering
of these events on longer time scales. The large amount of missing
data makes such analysis difficult, but the non-missing data is
clustered on time spans of 9 bins or so. Therefore, it seems to me
that with the right algorithm, it should be possible to estimate the
autocorrellation at lags of less than 9 bins. Does anyone know what
the right algorithm would be?