Dear All,
I am not an expert about time series, but I am given a time series to
analyze.
That time series stands for the list of individuals in contact with a
given individual at time t_i, where the ID of every individual is an
integer number. (let us not care right now about the meaning of being in
contact with in this context, since it does not matter for the discussion).
To fix the ideas, consider the following (I am tracking the contacts of
an individual whose ID is 1000)
c(1000,1100), c(1000,1100,1200),c(1000),c(NA), c(1000,1400)
t_1 , t_2 , t_3 , t_4 , t_5
i.e. at time t_i individual 1000 is in contact with individual 1100, at
time t_2 he is in contact also with individual 1200, at time t_3 he is
by himself (represented as the individual in contact by himself),
whereas at time t_4 I have no info about his state (missing info) and
finally at time t_5 he is in contact with individual 1400.
How would you analyze this series? I do not have a single number at
every time so I cannot assume that the series is the typical succession
{x_i} at time {t_i}.
Replacing the lists of individuals at time t_i with just the number of
individuals in contact with individual 1000 at time t_i throws away
valuable information (I cannot distinguish any more the situation at
time t_1 from that at time t_5).
If I use a hash (like those provided by the digest package) I can then
squeeze every list at time t_i into a string, but again I lose
information (e.g. I cannot tell any more than there is considerable
overlap in the situation at time t_1 and t_2).
Finally, I would like to stress that strictly speaking I do not have a
vector at every time t_i; indeed I do not have an object I can vary
continuously (individual 1000 either is in contact with individual 1100
or he is not) and on top of of that I do not have an obvious/uniquely
defined notion of distance between the time series at t_i and the one at
t_j.
Any suggestions are appreciated.
Many thanks
Lorenzo