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R: how to average within overlapping time periods

I have recently posted a similar question here, which was a bit oversimplified, though. Thus here we go again:

Assume I have a dataframe (dput output below) with time series data of many different variables (5 in this example, many more in the real data):

          date          a  b  c  d  e
1  2009-10-01 00:00:00 10 20 30 40 50
2  2009-10-01 01:00:00 11 21 31 41 51
3  2009-10-01 02:00:00 12 22 32 42 52
4  2009-10-01 03:00:00 13 23 33 43 53
5  2009-10-01 04:00:00 14 24 34 44 54
6  2009-10-01 05:00:00 15 25 35 45 55
7  2009-10-01 06:00:00 16 26 36 46 56
8  2009-10-01 07:00:00 17 27 37 47 57
9  2009-10-01 08:00:00 18 28 38 48 58
10 2009-10-01 09:00:00 19 29 39 49 59
11 2009-10-01 10:00:00 20 30 40 50 60
12 2009-10-01 11:00:00 21 31 41 51 61
13 2009-10-01 12:00:00 22 32 42 52 62
14 2009-10-01 13:00:00 23 33 43 53 63
15 2009-10-01 14:00:00 24 34 44 54 64
16 2009-10-01 15:00:00 25 35 45 55 65
17 2009-10-01 16:00:00 26 36 46 56 66
18 2009-10-01 17:00:00 27 37 47 57 67
19 2009-10-01 18:00:00 28 38 48 58 68
20 2009-10-01 19:00:00 29 39 49 59 69
21 2009-10-01 20:00:00 30 40 50 60 70
22 2009-10-01 21:00:00 31 41 51 61 71
23 2009-10-01 22:00:00 32 42 52 62 72
24 2009-10-01 23:00:00 33 43 53 63 73
25 2009-10-02 00:00:00 34 44 54 64 74

and another data frame "events" with different time periods defined by a start and stop date (3 here, many more in the real data):

   id       start                stop
1 AGH 2009-10-01 02:00:00 2009-10-01 04:00:00
2 TRG 2009-10-01 03:00:00 2009-10-01 10:00:00
3 ZUH 2009-10-01 03:00:00 2009-10-01 20:00:00

I would like to get a table of the mean values of the variables within the different events like this:

   id avg(y.a) avg(y.b) avg(y.c) avg(y.d) avg(y.e)
1 AGH     13.0     23.0     33.0     43.0     53.0
2 TRG     16.5     26.5     36.5     46.5     56.5
3 ZUH     21.5     31.5     41.5     51.5     61.5

I have learned from my previous post that I can do this using the sqldf package and a rather simple SQL statement:

means <- sqldf("
+     SELECT x.id, avg(y.a), avg(y.b), avg(y.c), avg(y.d), avg(y.e) 
+     FROM events as x, data as y 
+     WHERE y.date between x.start and x.stop 
+     GROUP BY x.id 
+ ")

However, as the real data contains many more columns to average, which are named differently in the various files I have to process, typing all the column names into the SQL statements becomes a bit tedious.

Thus I would prefer a solution in R, where I can simply refer to the columns by their number (data[2:100]) The difficulty is, though, that the time periods are non-continous and overlapping and the ids are character strings.

Any ideas how to do this would be much appreciated!

dput(data)

structure(list(date = structure(c(1254348000, 1254351600, 1254355200, 
1254358800, 1254362400, 1254366000, 1254369600, 1254373200, 1254376800, 
1254380400, 1254384000, 1254387600, 1254391200, 1254394800, 1254398400, 
1254402000, 1254405600, 1254409200, 1254412800, 1254416400, 1254420000, 
1254423600, 1254427200, 1254430800, 1254434400), class = c("POSIXct", 
"POSIXt"), tzone = "Europe/Berlin"), a = 10:34, b = 20:44, c = 30:54, 
    d = 40:64, e = 50:74), .Names = c("date", "a", "b", "c", 
"d", "e"), row.names = c(NA, -25L), class = "data.frame")

dput(events)

structure(list(id = structure(1:3, .Label = c("AGH", "TRG", "ZUH"
), class = "factor"), start = structure(c(1254355200, 1254358800, 
1254358800), class = c("POSIXct", "POSIXt"), tzone = "Europe/Berlin"), 
    stop = structure(c(1254362400, 1254384000, 1254420000), class = c("POSIXct", 
    "POSIXt"), tzone = "Europe/Berlin")), .Names = c("id", "start", 
"stop"), row.names = c(NA, -3L), class = "data.frame")