Back Transformation Techniques for The ATAforecasting

Source: R/ATA_Transform.R

The function provides the applicability of different types of back transformation techniques for the transformed data to which the Ata method will be applied. The ATA.BackTransform function works with many different types of inputs.

ATA.BackTransform(X, tMethod, tLambda, tShift, tbiasadj = FALSE, tfvar = NULL)

Arguments

X

a numeric vector or time series of class ts or msts for in-sample.

tMethod

Box-Cox power transformation family is consist of "Box_Cox", "Sqrt", "Reciprocal", "Log", "NegLog", "Modulus", "BickelDoksum", "Manly", "Dual", "YeoJohnson", "GPower", "GLog" in ATAforecasting package.

tLambda

Box-Cox power transformation family parameter. If NULL, data transformed before model is estimated.

tShift

Box-Cox power transformation family shifting parameter. If NULL, data transformed before model is estimated.

tbiasadj

Use adjusted back-transformed mean for Box-Cox transformations using forecast::BoxCox. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If tbiasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

tfvar

Optional parameter required if tbiasadj=TRUE. Can either be the forecast variance, or a list containing the interval level, and the corresponding upper and lower intervals.

Value

A list object consists of transformation parameters and transformed data. ATA.Transform is a list containing at least the following elements:

  • trfmX : Transformed data

  • tLambda : Box-Cox power transformation family parameter

  • tShift : Box-Cox power transformation family shifting parameter

References

#'Tukey JW (1957). “On the Comparative Anatomy of Transformations.” The Annals of Mathematical Statistics, 28(3), 602--632.

#'Box GEP, Cox DR (1964). “An Analysis of Transformations.” Journal of the Royal Statistical Society. Series B (Methodological), 26(2), 211--252.

#'Manly BFJ (1976). “Exponential data transformations.” Journal of the Royal Statistical Society Series D, 25(1), 37--42.

#'John JA, Draper NR (1980). “An alternative family of transformations.” Journal of the Royal Statistical Society Series C, 29(2), 190--197.

#'Bickel PJ, Doksum KA (1982). “An analysis of transformations revisited.” Journal of the American Statistical Association, 76(374), 296--311.

#'Sakia RM (1992). “The Box-Cox Transformation Technique: A Review.” Journal of the Royal Statistical Society Series D, 41(2), 169--178.

#'Guerrero VM (1993). “Time-series analysis supported by power transformations.” Journal of Forecasting, 12(1), 37--48.

#'Yeo I, Johnson RA (2000). “A New Family of Power Transformations to Improve Normality or Symmetry.” Biometrika, 87(4), 954--959.

#'Durbin BP, Hardin JS, Hawkins DM, Rocke DM (2002). “A variance-stabilizing transformation for gene-expression microarray data.” Bioinformatics, 18(1), 105--110.

#'Whittaker J, Whitehead C, Somers M (2005). “The neglog transformation and quantile regression for the analysis of a large credit scoring database.” Journal of the Royal Statistical Society Series C, 54(4), 863--878.

#'Yang Z (2005). “A modified family of power transformations.” Economics Letters, 92(1), 14--19.

#'Kelmansky DM, Martinez EJ, Leiva V (2013). “A new variance stabilizing transformation for gene expression data analysis.” Statistical Applications in Genetics and Molecular Biology, 12(6), 653--666.