Log-Interval Transformation for Constrained Interval Forecasting

The log_interval_vec() transformation constrains a forecast to an interval specified by an upper_limit and a lower_limit. The transformation provides similar benefits to log() transformation, while ensuring the inverted transformation stays within an upper and lower limit.

Usage

log_interval_vec(
  x,
  limit_lower = "auto",
  limit_upper = "auto",
  offset = 0,
  silent = FALSE
)

log_interval_inv_vec(x, limit_lower, limit_upper, offset = 0)

Arguments

x

A positive numeric vector.

limit_lower

A lower limit. Must be less than the minimum value. If set to "auto", selects zero.

limit_upper

An upper limit. Must be greater than the maximum value. If set to "auto", selects a value that is 10% greater than the maximum value.

offset

An offset to include in the log transformation. Useful when the data contains values less than or equal to zero.

silent

Whether or not to report the parameter selections as a message.

Value

A numeric vector of the transformed series.

Details

Log Interval Transformation

The Log Interval Transformation constrains values to specified upper and lower limits. The transformation maps limits to a function:

log(((x + offset) - a)/(b - (x + offset)))

where a is the lower limit and b is the upper limit

Inverse Transformation

The inverse transformation:

(b-a)*(exp(x)) / (1 + exp(x)) + a - offset

References

• Forecasting: Principles & Practices: Forecasts constrained to an interval

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 & Anomaly Cleaning for Time Series: ts_impute_vec(), ts_clean_vec()

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

Examples

library(dplyr)

values_trans <- log_interval_vec(1:10, limit_lower = 0, limit_upper = 11)
#> log_interval_vec(): 
#>  Using limit_lower: 0
#>  Using limit_upper: 11
#>  Using offset: 0
values_trans
#>  [1] -2.3025851 -1.5040774 -0.9808293 -0.5596158 -0.1823216  0.1823216
#>  [7]  0.5596158  0.9808293  1.5040774  2.3025851

values_trans_forecast <- c(values_trans, 3.4, 4.4, 5.4)

values_trans_forecast %>%
    log_interval_inv_vec(limit_lower = 0, limit_upper = 11) %>%
    plot()