Chain and rebase a price index

Chain a period-over-period index by taking the cumulative product of its values to turn it into a fixed-base (direct) index.

Unchain a fixed-base index by dividing its values for successive periods to get a period-over-period index.

Rebase a fixed-base index by dividing its values with the value of the index in the new base period.

Usage

chain(x, ...)

# Default S3 method
chain(x, ...)

# S3 method for class 'chainable_piar_index'
chain(x, link = rep(1, nlevels(x)), ...)

unchain(x, ...)

# Default S3 method
unchain(x, ...)

# S3 method for class 'direct_piar_index'
unchain(x, base = rep(1, nlevels(x)), ...)

rebase(x, ...)

# Default S3 method
rebase(x, ...)

# S3 method for class 'direct_piar_index'
rebase(x, base = rep(1, nlevels(x)), ...)

Arguments

x: A price index, as made by, e.g., elemental_index().
...: Further arguments passed to or used by methods.
link: A numeric vector, or something that can coerced into one, of link values for each level in x. The default is a vector of 1s so that no linking is done.
base: A numeric vector, or something that can coerced into one, of base-period index values for each level in x. The default is a vector of 1s so that the base period remains the same. If base is a length-one character vector giving a time period of x then the index values for this time period are used as the base-period values.

Value

chain() and rebase() return a fixed-base index that inherits from direct_piar_index.

unchain() returns a period-over-period index that inherits from chainable_piar_index.

Details

The default methods attempt to coerce x into an index with as_index() prior to chaining/unchaining/rebasing.

Chaining an index takes the cumulative product of the index values for each level; this is roughly the same as t(apply(as.matrix(x), 1, cumprod)) * link. Unchaining does the opposite, so these are inverse operations. Note that unchaining a period-over-period index does nothing, as does chaining a fixed-base index.

Rebasing a fixed-base index divides the values for each level of this index by the corresponding values for each level in the new base period. It's roughly the same as as.matrix(x) / base. Like unchaining, rebasing a period-over-period index does nothing.

Percent-change contributions are removed when chaining/unchaining/rebasing an index as it's not usually possible to update them correctly.

Examples

index <- as_index(matrix(1:9, 3))

# Make period 0 the fixed base period

chain(index)
#> Fixed-base price index for 3 levels over 3 time periods 
#>   1  2   3
#> 1 1  4  28
#> 2 2 10  80
#> 3 3 18 162

# Chaining and unchaining reverse each other

all.equal(index, unchain(chain(index)))
#> [1] TRUE

# Change the base period to period 2 (note the
# loss of information for period 0)

index <- chain(index)
rebase(index, index[, 2])
#> Fixed-base price index for 3 levels over 3 time periods 
#>           1 2 3
#> 1 0.2500000 1 7
#> 2 0.2000000 1 8
#> 3 0.1666667 1 9