With the exception of
vignette("spatial-price-index"), all the examples so far
have revolved around aggregating over the levels of a price index for
each time period. Although this is the core workflow in this package, it
is also useful to be able to aggregate over the time periods for each
level of an index to turn a monthly or quarterly index into an annual
index.
Let’s modify the example in vignette("adjust-weights")
by adding an additional eight quarters to make three years of data.
set.seed(54321)
library(piar)
# Make an aggregation structure.
# 1
# |-----------|-----------|
# 11 12 13
# |---+---| |---+---| |---+---|
# 111 121 121 122 131 132
pias <- data.frame(
level1 = rep(1, 12),
level2 = rep(c(11, 12, 13), each = 4),
level3 = rep(c(111, 112, 121, 122, 131, 132), each = 2),
ea = sprintf("B%02d", 1:12),
weight = 1:12
) |>
as_aggregation_structure()
pias## Aggregation structure for 12 elemental aggregates with 3 levels above the elemental aggregates
## level1 level2 level3 ea weight
## 1 1 11 111 B01 1
## 2 1 11 111 B02 2
## 3 1 11 112 B03 3
## 4 1 11 112 B04 4
## 5 1 12 121 B05 5
## 6 1 12 121 B06 6
## 7 1 12 122 B07 7
## 8 1 12 122 B08 8
## 9 1 13 131 B09 9
## 10 1 13 131 B10 10
## 11 1 13 132 B11 11
## 12 1 13 132 B12 12# Make elemental indexes over 3 years and aggregate.
quarterly_index <- matrix(
runif(12 * 12, 0.4, 1.2),
nrow = 12,
dimnames = list(sprintf("B%02d", 1:12), paste0("Q", 1:12))
) |>
as_index() |>
aggregate(pias)
head(quarterly_index)## Period-over-period price index for 6 levels over 12 time periods
## Q1 Q2 Q3 Q4 Q5 Q6 Q7
## 1 0.6847172 0.7513116 0.8602744 0.9150072 0.6691529 0.7621597 0.7928512
## 11 0.6442816 0.9426238 0.9800151 0.9787698 0.9366504 0.8698449 0.8068903
## 12 0.6553744 0.8448298 0.7877433 0.7364719 0.6864661 0.6092876 0.5790867
## 13 0.7125093 0.6568730 0.8763973 1.0105002 0.5713334 0.7912029 0.8792723
## 111 0.7802316 0.7678844 0.8888722 1.0294469 0.9856799 1.0533765 1.1007037
## 112 0.5860173 1.0423311 1.0183284 0.9601751 0.9173623 0.7922671 0.6417663
## Q8 Q9 Q10 Q11 Q12
## 1 0.9285013 0.7802293 0.8192686 0.7150868 0.9343166
## 11 1.0502027 0.8297739 0.9545600 0.7823591 0.8891911
## 12 0.7510670 1.0351129 0.6936704 0.5073677 0.7432221
## 13 0.9130143 0.6873897 0.7607797 0.7188072 1.0262155
## 111 1.1442371 0.7836807 1.0508585 0.5157759 1.1069026
## 112 0.9595630 0.8827540 0.8562962 1.1161902 0.7632120The conventional way to turn a quarterly arithmetic index into an annual one is to take the (unweighted) arithmetic mean of the index values over each year and rebase to a new base year.
## Fixed-base price index for 6 levels over 3 time periods
## Q1 Q5 Q9
## 1 1 0.3875906 0.17112143
## 11 1 0.7431798 0.46232765
## 12 1 0.2497373 0.07096693
## 13 1 0.3687070 0.14792335
## 111 1 0.9971250 0.72915914
## 112 1 0.6323628 0.34588738It’s worth not that, at least with an arithmetic index, the aggregation properties of the index continue to hold after price-updating the weights.
annual_pias <- pias |>
update(annual_index, period = "Q1")
annual_index <- annual_index |>
rebase("Q1")
annual_index |>
aggregate(annual_pias) |>
all.equal(annual_index)## [1] TRUEThis means that, for example, the workflow in
vignette("contributions") for determining, say, the
quarter-over-quarter contribution of the level 2 indexes to top-level
index remains the same.
# Reuse the reset_contrib() function from the other vignette.
reset_contrib <- function(index) {
contrib_matrix <- as.matrix(index) - 1
for (l in levels(index)) {
contrib(index, l) <- contrib_matrix[l, , drop = FALSE]
}
index
}
annual_index |>
unchain() |>
reset_contrib() |>
aggregate(cut(annual_pias, 2)) |>
contrib()## Q1 Q5 Q9
## 11 0 -0.03908184 -0.1102682
## 12 0 -0.24028499 -0.1477187
## 13 0 -0.33304262 -0.3005126