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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.