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# BOXCOX

Attachment | Size | |
---|---|---|

BoxCox.xlsx |

Returns the **Box-Cox ^{i}** transformation of the input data point(s).

## Syntax

**BOXCOX**(

**X**,

**Alpha**,

**Lambda**,

**Return_type**)

**X**

the real number for which we compute the transformation.

**Alpha**

is the input shift parameter for X. If omitted, the default value is 0.

**Lambda**

is the input power parameter of the transformation, on a scale from 1 to 0. If omitted, the default value of 0 is assumed.

**Return_type** is a number that determines the type of return value: 1 (or missing)= **Box-Cox** , 2= Inverse **Box-Cox**, 3= LLF^{i} of **Box-Cox**.

RETURN_TYPE | NUMBER RETURNED |
---|---|

1 or omitted | Box-Cox Transform |

2 | Inverse of Box-Cox transform |

3 | LLF of Box-Cox transform |

## Remarks

**Box-Cox**transform is perceived as a useful data (pre)processing technique used to stabilize variance and make the data more normally distributed.-
The
**Box-Cox**transformation is defined as follows:Where:

- is the value of the input time series at time
- is the input scalar value of the Box-Cox transformation
- is the shift parameter
- for all t values.

- The BOXCOX function accepts a single value or an array of values for X.
- The shift parameter must be large enough to make all the values of X positive.

## Examples

**Example 1: **

A | B | C | D | |
---|---|---|---|---|

1 | Date | Data | ||

2 | January 10, 2008 | -0.30 | 0.89 | -0.30 |

3 | January 11, 2008 | -1.28 | 0.20 | -1.28 |

4 | January 12, 2008 | 0.24 | 1.18 | 0.24 |

5 | January 13, 2008 | 1.28 | 1.63 | 1.28 |

6 | January 14, 2008 | 1.20 | 1.60 | 1.2 |

7 | January 15, 2008 | 1.73 | 1.80 | 1.73 |

8 | January 16, 2008 | -2.18 | -0.97 | -2.18 |

9 | January 17, 2008 | -0.23 | 0.93 | -0.23 |

10 | January 18, 2008 | 1.10 | 1.56 | 1.1 |

11 | January 19, 2008 | -1.09 | 0.36 | -1.09 |

12 | January 20, 2008 | -0.69 | 0.65 | -0.69 |

13 | January 21, 2008 | -1.69 | -0.20 | -1.69 |

14 | January 22, 2008 | -1.85 | -0.40 | -1.85 |

15 | January 23, 2008 | -0.98 | 0.45 | -0.98 |

16 | January 24, 2008 | -0.77 | 0.60 | -0.77 |

17 | January 25, 2008 | -0.30 | 0.89 | -0.3 |

18 | January 26, 2008 | -1.28 | 0.20 | -1.28 |

19 | January 27, 2008 | 0.24 | 1.18 | 0.24 |

20 | January 28, 2008 | 1.28 | 1.63 | 1.28 |

21 | January 29, 2008 | 1.20 | 1.60 | 1.2 |

22 | January 30, 2008 | 1.73 | 1.80 | 1.2 |

23 | January 31, 2008 | -2.18 | -0.97 | -2.81 |

24 | February 1, 2008 | -0.23 | 0.93 | -0.23 |

25 | February 2, 2008 | 1.10 | 1.56 | 1.1 |

26 | February 3, 2008 | -1.09 | 0.36 | -1.09 |

27 | February 4, 2008 | -0.69 | 0.65 | -0.69 |

28 | February 5, 2008 | -1.69 | -0.20 | -1.69 |

29 | February 6, 2008 | -1.85 | -0.40 | -1.85 |

30 | February 7, 2008 | -0.98 | 0.45 | -0.98 |

Formula | Description (Result) | |
---|---|---|

=BOXCOX($B$2:$B$30,3,0.5,3) | LLF Boxcoc (-33.35) |

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

Attachment | Size |
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BoxCox.xlsx | 21.44 KB |