Here's a solution using xts:
x <- structure(c(867L, 891L, 901L, 991L, 1085L, 1114L, 1117L, 1151L,
1174L, 1268L, 1384L, 1403L, 1550L, 1596L, 1608L), .Dim = c(15L, 1L),
index = structure(c(1280960887, 1280964672, 1280966285,
1280997350, 1281014882, 1281017687, 1281018106, 1281023184, 1281025529,
1281050369, 1281096942, 1281108126, 1281176749, 1281207496, 1281215744),
tzone = "", tclass = c("POSIXct", "POSIXt")), class = c("xts", "zoo"),
.indexCLASS = c("POSIXct", "POSIXt"), tclass = c("POSIXct", "POSIXt"),
.indexTZ = "", tzone = "")
# first count the number of observations each day
xd <- apply.daily(x, length)
# now sum the counts over a 2-day rolling window
x2d <- rollapply(xd, 2, sum)
# align times at the end of the period (if you want)
y <- align.time(x2d, n=60*60*24) # n is in seconds
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