Using accumulate function with second to last value as .init argument - r

Question

I have recently come across an interesting question of calculating a vector values using its penultimate value as .init argument plus an additional vector's current value. Here is the sample data set:
set.seed(13)
dt <- data.frame(id = rep(letters[1:2], each = 5), time = rep(1:5, 2), ret = rnorm(10)/100)
dt$ind <- if_else(dt$time == 1, 120, if_else(dt$time == 2, 125, as.numeric(NA)))
id time ret ind
1 a 1 0.005543269 120
2 a 2 -0.002802719 125
3 a 3 0.017751634 NA
4 a 4 0.001873201 NA
5 a 5 0.011425261 NA
6 b 1 0.004155261 120
7 b 2 0.012295066 125
8 b 3 0.002366797 NA
9 b 4 -0.003653828 NA
10 b 5 0.011051443 NA
What I would like to calculate is:
ind_{t} = ind_{t-2}*(1+ret_{t})
I tried the following code. Since .init is of no use here I tried the nullify the original .init and created a virtual .init but unfortunately it won't drag the newly created values (from third row downward) into calculation:
dt %>%
group_by(id) %>%
mutate(ind = c(120, accumulate(3:n(), .init = 125,
~ .x * 1/.x * ind[.y - 2] * (1 + ret[.y]))))
# A tibble: 10 x 4
# Groups: id [2]
id time ret ind
<chr> <int> <dbl> <dbl>
1 a 1 0.00554 120
2 a 2 -0.00280 125
3 a 3 0.0178 122.
4 a 4 0.00187 125.
5 a 5 0.0114 NA
6 b 1 0.00416 120
7 b 2 0.0123 125
8 b 3 0.00237 120.
9 b 4 -0.00365 125.
10 b 5 0.0111 NA
I was wondering if there was a tweak I could make to this code and make it work completely.
I would appreciate your help greatly in advance

Answer 1

Use a state vector consisting of the current value of ind and the prior value of ind. That way the prior state contains the second prior value of ind. We encode that into complex values with the real part equal to ind and the imaginary part equal to the prior value of ind. At the end we take the real part.
library(dplyr)
library(purrr)
dt %>%
group_by(id) %>%
mutate(result = c(ind[1],
Re(accumulate(.x = tail(ret, -2),
.f = ~ Im(.x) * (1 + .y) + Re(.x) * 1i,
.init = ind[2] + ind[1] * 1i)))) %>%
ungroup
giving:
# A tibble: 10 x 5
id time ret ind result
<chr> <int> <dbl> <dbl> <dbl>
1 a 1 0.00554 120 120
2 a 2 -0.00280 125 125
3 a 3 0.0178 NA 122.
4 a 4 0.00187 NA 125.
5 a 5 0.0114 NA 124.
6 b 1 0.00416 120 120
7 b 2 0.0123 125 125
8 b 3 0.00237 NA 120.
9 b 4 -0.00365 NA 125.
10 b 5 0.0111 NA 122.
Variation
This variation eliminates the complex numbers and uses a vector of 2 elements in place of each complex number with the first number corresponding to the real part in the prior solution and the second number of each pair corresponding to the imaginary part. This could be extended to cases where we need more than 2 numbers per state and where the dependence involves all of the last N values but for the question here there is the downside of the extra line of code to extract the result from the list of pairs of numbers which is more involved than using Re in the prior solution.
dt %>%
group_by(id) %>%
mutate(result = c(ind[1],
accumulate(.x = tail(ret, -2),
.f = ~ c(.x[2] * (1 + .y), .x[1]),
.init = ind[2:1])),
result = map_dbl(result, first)) %>%
ungroup
Check
We check that the results above are correct. Alternately this could be used as a straight forward solution.
calc <- function(ind, ret) {
for(i in seq(3, length(ret))) ind[i] <- ind[i-2] * (1 + ret[i])
ind
}
dt %>%
group_by(id) %>%
mutate(result = calc(ind, ret)) %>%
ungroup
giving:
# A tibble: 10 x 5
id time ret ind result
<chr> <int> <dbl> <dbl> <dbl>
1 a 1 0.00554 120 120
2 a 2 -0.00280 125 125
3 a 3 0.0178 NA 122.
4 a 4 0.00187 NA 125.
5 a 5 0.0114 NA 124.
6 b 1 0.00416 120 120
7 b 2 0.0123 125 125
8 b 3 0.00237 NA 120.
9 b 4 -0.00365 NA 125.
10 b 5 0.0111 NA 122.

Answer 2

I would have done it by creating dummy groups for each sequence, so that it can be done for any number of 'N'. Demonstrating it on a new elaborated data
df <- data.frame(
stringsAsFactors = FALSE,
grp = c("a","a","a","a",
"a","a","a","a","a","b","b","b","b","b",
"b","b","b","b"),
rate = c(0.082322056,
0.098491104,0.07294593,0.08741672,0.030179747,
0.061389031,0.011232314,0.08553277,0.091272669,
0.031577847,0.024039791,0.091719552,0.032540636,
0.020411727,0.094521716,0.081729178,0.066429708,
0.04985793),
ind = c(11000L,12000L,
13000L,NA,NA,NA,NA,NA,NA,10000L,13000L,12000L,
NA,NA,NA,NA,NA,NA)
)
df
#> grp rate ind
#> 1 a 0.08232206 11000
#> 2 a 0.09849110 12000
#> 3 a 0.07294593 13000
#> 4 a 0.08741672 NA
#> 5 a 0.03017975 NA
#> 6 a 0.06138903 NA
#> 7 a 0.01123231 NA
#> 8 a 0.08553277 NA
#> 9 a 0.09127267 NA
#> 10 b 0.03157785 10000
#> 11 b 0.02403979 13000
#> 12 b 0.09171955 12000
#> 13 b 0.03254064 NA
#> 14 b 0.02041173 NA
#> 15 b 0.09452172 NA
#> 16 b 0.08172918 NA
#> 17 b 0.06642971 NA
#> 18 b 0.04985793 NA
library(tidyverse)
N = 3
df %>% group_by(grp) %>%
group_by(d = row_number() %% N, .add = TRUE) %>%
mutate(ind = accumulate(rate[-1] + 1, .init = ind[1], ~ .x * .y))
#> # A tibble: 18 x 4
#> # Groups: grp, d [6]
#> grp rate ind d
#> <chr> <dbl> <dbl> <dbl>
#> 1 a 0.0823 11000 1
#> 2 a 0.0985 12000 2
#> 3 a 0.0729 13000 0
#> 4 a 0.0874 11962. 1
#> 5 a 0.0302 12362. 2
#> 6 a 0.0614 13798. 0
#> 7 a 0.0112 12096. 1
#> 8 a 0.0855 13420. 2
#> 9 a 0.0913 15057. 0
#> 10 b 0.0316 10000 1
#> 11 b 0.0240 13000 2
#> 12 b 0.0917 12000 0
#> 13 b 0.0325 10325. 1
#> 14 b 0.0204 13265. 2
#> 15 b 0.0945 13134. 0
#> 16 b 0.0817 11169. 1
#> 17 b 0.0664 14147. 2
#> 18 b 0.0499 13789. 0
Alternate answer in dplyr (using your own data modified a bit only)
set.seed(13)
dt <- data.frame(id = rep(letters[1:2], each = 5), time = rep(1:5, 2), ret = rnorm(10)/100)
dt$ind <- ifelse(dt$time == 1, 12000, ifelse(dt$time == 2, 12500, as.numeric(NA)))
library(dplyr, warn.conflicts = F)
dt %>% group_by(id) %>%
group_by(d= row_number() %% 2, .add = TRUE) %>%
mutate(ind = cumprod(1 + duplicated(id) * ret)* ind[1])
#> # A tibble: 10 x 5
#> # Groups: id, d [4]
#> id time ret ind d
#> <chr> <int> <dbl> <dbl> <dbl>
#> 1 a 1 0.00554 12000 1
#> 2 a 2 -0.00280 12500 0
#> 3 a 3 0.0178 12213. 1
#> 4 a 4 0.00187 12523. 0
#> 5 a 5 0.0114 12353. 1
#> 6 b 1 0.00416 12000 0
#> 7 b 2 0.0123 12500 1
#> 8 b 3 0.00237 12028. 0
#> 9 b 4 -0.00365 12454. 1
#> 10 b 5 0.0111 12161. 0