Aggregating over subperiods

In piar: Price Index Aggregation

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

# 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)

The 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.

annual_index <- chain(quarterly_index) |>
  mean(window = 4)

annual_index |>
  rebase("Q1") |>
  head()

It's worth noting 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)

This 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.

annual_index |>
  unchain() |>
  set_contrib_from_index() |>
  aggregate(cut(annual_pias, 2)) |>
  contrib()

piar documentation built on April 3, 2025, 7:38 p.m.