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Divisia second moments

Source: R/analyses.R
dmai_moments.Rd

dmai_moments() gives the Divisia mean and variance of the growth rates of the components at every date (Theil 1967; Barnett and Serletis 1990): $$\kappa_t = \sum_i \bar{s}_{it}\,\Delta\log x_{it}, \qquad K_t = \sum_i \bar{s}_{it}\left(\Delta\log x_{it} - \kappa_t\right)^2,$$ and the same for the user costs. A large variance means the components grow at very different rates, so that the choice of weights matters and the simple sum is a poor guide; Barnett and Serletis use it as a diagnostic of aggregation error.

Usage

dmai_moments(.data, ...)

# Default S3 method
dmai_moments(
  .data,
  ...,
  date = "Date",
  x = NULL,
  r = NULL,
  user_cost = NULL,
  benchmark = NULL,
  percent = TRUE
)

# S3 method for class 'dmai_index'
dmai_moments(.data, ...)

Arguments

.data

a data frame as in dmai(), or a result of dmai(..., as_dt = FALSE).

...

further arguments of dmai() (date, x, r, user_cost, benchmark, percent) when .data is a data frame.

date

name of the date column (default "Date").

x

names of the quantity columns (default NULL: x1, x2, ...).

r

names of the rate columns, in the order of x (default NULL: r1, r2, ...).

user_cost

names of columns that give the user costs directly, in the order of x (default NULL: computed from the rates). The rates are then needed only for "CE".

benchmark

the benchmark rate: NULL (default, the largest component rate), a column name, a number or one value per row of .data, in the units of the rates.

percent

logical; are the rates in percent (default TRUE) or decimal?

Value

An object of class c("dmai_moments", "dmai_result", "list"): moments (a data.table with the date, growth = \(100\kappa_t\), variance = \(10^4K_t\), sd, price_growth and price_variance) and settings. plot() draws the standard deviation over time.

References

Barnett, W. A. and Serletis, A. (1990). A dispersion-dependency diagnostic test for aggregation error: with applications to monetary economics and income distribution. Journal of Econometrics, 43(1–2), 5–34. doi:10.1016/0304-4076(90)90104-2

Theil, H. (1967). Economics and Information Theory. North-Holland, Amsterdam.

See also

Other dmai analyses: dmai(), dmai_compare(), dmai_user_cost()

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(money_sim)
m <-
  dmai_moments(
      .data     = money_sim
    , benchmark = "rb"
    )
m
#> Divisia second moments of 8 components, 240 dates
#> =================================================
#> Standard deviation of component growth (percent): mean 1.291, largest 2.166 at 2006-10-01
#> 
#>            Date  growth variance     sd price_growth price_variance
#>          <Date>   <num>    <num>  <num>        <num>          <num>
#>   1: 2005-01-01      NA       NA     NA           NA             NA
#>   2: 2005-02-01  0.8504   2.9412 1.7150       0.2897          1.660
#>   3: 2005-03-01  1.7329   0.5433 0.7371      -4.0886          2.806
#>   4: 2005-04-01 -0.2494   0.8553 0.9248      -0.5237         17.461
#>   5: 2005-05-01  0.3359   2.1111 1.4530       2.8567         33.914
#>  ---                                                               
#> 236: 2024-08-01  0.1823   2.2071 1.4856      -0.6872          7.943
#> 237: 2024-09-01  0.5280   2.8598 1.6911      -4.3389          7.649
#> 238: 2024-10-01  0.9856   2.6784 1.6366      -1.8756         10.041
#> 239: 2024-11-01  2.0063   2.9887 1.7288       1.1803          9.420
#> 240: 2024-12-01  0.6266   3.3179 1.8215      -2.5608          7.970
#> 
#> Sources: Theil (1967); Barnett and Serletis (1990). Full references:
#> dmai_cite(x).
plot(x = m)