Box Cox Transformation

This is mainly a wrapper for the BoxCox transformation from the forecast R package. The box_cox_vec() function performs the transformation. box_cox_inv_vec() inverts the transformation. auto_lambda() helps in selecting the optimal lambda value.

Usage

box_cox_vec(x, lambda = "auto", silent = FALSE)

box_cox_inv_vec(x, lambda)

auto_lambda(
  x,
  method = c("guerrero", "loglik"),
  lambda_lower = -1,
  lambda_upper = 2
)

Arguments

x

A numeric vector.

lambda

The box cox transformation parameter. If set to "auto", performs automated lambda selection using auto_lambda().

silent

Whether or not to report the automated lambda selection as a message.

method

The method used for automatic lambda selection. Either "guerrero" or "loglik".

lambda_lower

A lower limit for automatic lambda selection

lambda_upper

An upper limit for automatic lambda selection

Value

Returns a numeric vector that has been transformed.

Details

The Box Cox transformation is a power transformation that is commonly used to reduce variance of a time series.

Automatic Lambda Selection

If desired, the lambda argument can be selected using auto_lambda(), a wrapper for the Forecast R Package's forecast::BoxCox.lambda() function. Use either of 2 methods:

1. "guerrero" - Minimizes the non-seasonal variance

2. "loglik" - Maximizes the log-likelihood of a linear model fit to x

References

• Forecast R Package

• Forecasting: Principles & Practices: Transformations & Adjustments

• Guerrero, V.M. (1993) Time-series analysis supported by power transformations. Journal of Forecasting, 12, 37--48.

See also

• Box Cox Transformation: box_cox_vec()

• Lag Transformation: lag_vec()

• Differencing Transformation: diff_vec()

• Rolling Window Transformation: slidify_vec()

• Loess Smoothing Transformation: smooth_vec()

• Fourier Series: fourier_vec()

• Missing Value Imputation for Time Series: ts_impute_vec(), ts_clean_vec()

Other common transformations to reduce variance: log(), log1p() and sqrt()

Examples

library(dplyr)
d10_daily <- m4_daily %>% dplyr::filter(id == "D10")

# --- VECTOR ----

value_bc <- box_cox_vec(d10_daily$value)
#> box_cox_vec(): Using value for lambda: 1.25119350454964
value    <- box_cox_inv_vec(value_bc, lambda = 1.25119350454964)

# --- MUTATE ----

m4_daily %>%
    dplyr::group_by(id) %>%
    dplyr::mutate(value_bc = box_cox_vec(value))
#> box_cox_vec(): Using value for lambda: 1.25119350454964
#> box_cox_vec(): Using value for lambda: 0.0882021886505848
#> box_cox_vec(): Using value for lambda: 1.99992424816297
#> box_cox_vec(): Using value for lambda: 0.401716085353735
#> # A tibble: 9,743 × 4
#> # Groups:   id [4]
#>    id    date       value value_bc
#>    <fct> <date>     <dbl>    <dbl>
#>  1 D10   2014-07-03 2076.   11303.
#>  2 D10   2014-07-04 2073.   11284.
#>  3 D10   2014-07-05 2049.   11116.
#>  4 D10   2014-07-06 2049.   11117.
#>  5 D10   2014-07-07 2006.   10829.
#>  6 D10   2014-07-08 2018.   10905.
#>  7 D10   2014-07-09 2019.   10915.
#>  8 D10   2014-07-10 2007.   10836.
#>  9 D10   2014-07-11 2010    10854.
#> 10 D10   2014-07-12 2002.   10796.
#> # ℹ 9,733 more rows