Calculate annualized rate of change (ARC)

Source: R/change.R

Calculate annualized rate of change from one vector which includes numeric year and another vector which includes values of some measure for those years.

arc(years, values, denominator = 100)

Arguments

years

[numeric()]
Years corresponding to input values
values

[numeric()]
Input values for some measure evaluated over time
denominator

[numeric()]
Default to 100 for percent (ex: 20%). Specify denominator = 1 to get annualized rate of change as a decimal (ex: 0.20).

Value

[numeric()]
Annualized rate of change for the intervals between elements of years.

Details

ARC for the period between years i and j is calculated as: $$arc[i,j] = 100 * ln(value_j / value_i) / (year_j - year_i)$$ Index is such that for index i, output[i] is arc for period years[i - 1] to years[i] and the first entry in the output is NA. This function does not sort years so users should check inputs are ordered correctly.

See also

  • Preston Demography textbook Chapter 1

  • https://www.un.org/esa/sustdev/natlinfo/indicators/methodology_sheets/demographics/population_growth_rate.pdf

Examples

# vectors
arc(years = c(2000, 2005, 2010), values = c(10, 20, 25))

#> [1]        NA 13.862944  4.462871

# data.table
library(data.table)
dt <- data.table(
  year = c(2000, 2005, 2010),
  val = c(10, 20, 25)
)
dt[, arc := arc(years = year, values = val)]

#>    year val       arc
#> 1: 2000  10        NA
#> 2: 2005  20 13.862944
#> 3: 2010  25  4.462871