Box Cox Transformation

BoxCox() returns a transformation of the input variable using a Box-Cox transformation. InvBoxCox() reverses the transformation.

BoxCox(x, lambda)

InvBoxCox(x, lambda, biasadj = FALSE, fvar = NULL)

Arguments

x	a numeric vector or time series of class `ts`.
lambda	transformation parameter. If `lambda = "auto"`, then the transformation parameter lambda is chosen using BoxCox.lambda.
biasadj	Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.
fvar	Optional parameter required if biasadj=TRUE. Can either be the forecast variance, or a list containing the interval `level`, and the corresponding `upper` and `lower` intervals.

Value

a numeric vector of the same length as x.

Details

The Box-Cox transformation is given by $$f_\lambda(x) =\frac{x^\lambda - 1}{\lambda}$$ if $\lambda\ne0$. For $\lambda=0$, $$f_0(x)=\log(x)$$.

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211--246.

Author

Rob J Hyndman & Mitchell O'Hara-Wild

Examples


lambda <- BoxCox.lambda(lynx)
lynx.fit <- ar(BoxCox(lynx,lambda))
plot(forecast(lynx.fit,h=20,lambda=lambda))
#> Error in NextMethod(.Generic): cannot assign 'tsp' to zero-length vector