# Documentation

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# boxcox

Box-Cox transformation

## Syntax

```[transdat, lambda] = boxcox(data)
[transfts, lambda] = boxcox(tsobj)
transdat = boxcox(lambda, data)
transfts = boxcox(lambda, tsobj)
```

## Arguments

 `data` Data vector. Must be positive and specified as a column data vector. `tsobj` Financial time series object.

## Description

`boxcox` transforms nonnormally distributed data to a set of data that has approximately normal distribution. The Box-Cox transformation is a family of power transformations.

If λ is not = `0`, then

`$data\left(\lambda \right)=\frac{dat{a}^{\lambda }-1}{\lambda }$`

If λ is = `0`, then

`$data\left(\lambda \right)=\mathrm{log}\left(data\right)$`

The logarithm is the natural logarithm (log base e). The algorithm calls for finding the λ value that maximizes the Log-Likelihood Function (LLF). The search is conducted using `fminsearch`.

`[transdat, lambda] = boxcox(data)` transforms the data vector `data` using the Box-Cox transformation method into `transdat`. It also estimates the transformation parameter λ.

`[transfts, lambda] = boxcox(tsojb)` transforms the financial time series object `tsobj` using the Box-Cox transformation method into `transfts`. It also estimates the transformation parameter λ.

If the input data is a vector, `lambda` is a scalar. If the input is a financial time series object, `lambda` is a structure with fields similar to the components of the object; for example, if the object contains series names `Open` and `Close`, `lambda` has fields `lambda.Open` and `lambda.Close`.

`transdat = boxcox(lambda, data)` and ```transfts = boxcox(lambda, tsobj)``` transform the data using a certain specified λ for the Box-Cox transformation. This syntax does not find the optimum λ that maximizes the LLF.