# BoxCox: Box Cox Transformation In forecast: Forecasting Functions for Time Series and Linear Models

 BoxCox R Documentation

## Box Cox Transformation

### Description

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

### Usage

```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 (with a lower bound of -0.9) `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.

### Details

The Box-Cox transformation (as given by Bickel & Doksum 1981) is given by

f(x;lambda)=sign(x)(|x|^lambda - 1)/lambda

if lambda is not equal to 0. For lambda=0,

f(x;0)=log(x)

.

### Value

a numeric vector of the same length as x.

### Author(s)

Rob J Hyndman & Mitchell O'Hara-Wild

### References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211–246. Bickel, P. J. and Doksum K. A. (1981) An Analysis of Transformations Revisited. JASA 76 296-311.

`BoxCox.lambda`

### Examples

```
lambda <- BoxCox.lambda(lynx)
lynx.fit <- ar(BoxCox(lynx,lambda))
plot(forecast(lynx.fit,h=20,lambda=lambda))

```

forecast documentation built on July 25, 2022, 5:05 p.m.