Mutiple covariance matrix with high-frecuency data using R - r

Question

I'm working with high-frequency data which contains 2 million observations. Now, I need to calculate the daily Realized Covariance matrix, defined as:
Let be an intraday prices vector and the number of intraday prices
My data has the following structure:
Year Month Day FivMin A B C D
2000 1 1 1 1 2 3 4
2000 1 1 2 2 3 0 1
2000 1 1 3 3 4 1 2
2000 1 1 4 0 1 2 3
2000 1 2 1 1 2 3 4
2000 1 2 2 5 3 4 1
2000 1 2 3 3 0 1 2
2000 1 2 4 4 1 9 3
2000 1 3 1 1 2 3 4
2000 1 3 2 0 1 7 1
2000 1 3 3 3 4 1 2
2000 1 3 4 1 -2 2 3
2000 1 4 1 0 2 3 4
2000 1 4 2 2 1 4 1
2000 1 4 3 3 0 1 2
2000 1 4 4 0 2 2 3
2000 1 5 1 1 2 3 4
2000 1 5 2 2 3 4 1
2000 1 5 3 0 -1 1 2
2000 1 5 4 9 1 2 3
Variables A, B, C, and D represent prices recorded each five minutes. So my first idea is to use group_by with the variables Year, Month, and Day in order to create the matrix. After this, I need to calculate the Realized Cov for each day.
For example, for the first day my Realized Cov would be:
this operation has to be repeated every day. I do not if there is a package for this problem or not. Maybe, it is better to use a loop.
Thanks for helping me.

Answer 1

Here is a base R solution using split (for grouping) + tcrossprod (for cov matrix)
res <- lapply(split(df,df[c("Year","Month","Day")]),
function(x) tcrossprod(t(x[c("A","B","C","D")])))
such that
> res
$`2000.1.1`
A B C D
A 14 20 6 12
B 20 30 12 22
C 6 12 14 20
D 12 22 20 30
$`2000.1.2`
A B C D
A 51 21 62 27
B 21 14 27 14
C 62 27 107 45
D 27 14 45 30
$`2000.1.3`
A B C D
A 11 12 8 13
B 12 25 13 11
C 8 13 63 27
D 13 11 27 30
$`2000.1.4`
A B C D
A 13 2 11 8
B 2 9 14 15
C 11 14 30 24
D 8 15 24 30
$`2000.1.5`
A B C D
A 86 17 29 33
B 17 15 19 12
C 29 19 30 24
D 33 12 24 30
DATA
df <- structure(list(Year = c(2000L, 2000L, 2000L, 2000L, 2000L, 2000L,
2000L, 2000L, 2000L, 2000L, 2000L, 2000L, 2000L, 2000L, 2000L,
2000L, 2000L, 2000L, 2000L, 2000L), Month = c(1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L
), Day = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L,
4L, 4L, 4L, 5L, 5L, 5L, 5L), FivMin = c(1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L), A = c(1L,
2L, 3L, 0L, 1L, 5L, 3L, 4L, 1L, 0L, 3L, 1L, 0L, 2L, 3L, 0L, 1L,
2L, 0L, 9L), B = c(2L, 3L, 4L, 1L, 2L, 3L, 0L, 1L, 2L, 1L, 4L,
-2L, 2L, 1L, 0L, 2L, 2L, 3L, -1L, 1L), C = c(3L, 0L, 1L, 2L,
3L, 4L, 1L, 9L, 3L, 7L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L
), D = c(4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L,
1L, 2L, 3L, 4L, 1L, 2L, 3L)), class = "data.frame", row.names = c(NA,
-20L))