# Documentation/Calc Functions/FORECAST.ETS.PI.MULT

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## Function name:

FORECAST.ETS.PI.MULT

## Category:

Statistical Analysis

## Summary:

Calculates the prediction interval(s) for multiplicative forecast based on the historical data using ETS (Exponential Triple Smoothing) or EDS (Exponential Double Smoothing) algorithms. EDS is used when argument **period_length** is 0, otherwise ETS is used.

## Syntax:

FORECAST.ETS.PI.MULT(**target**, **values**, **timeline**, [**confidence_level**], [**period_length**], [**data_completion**], [**aggregation**])

## Returns:

Returns a real number which is the prediction interval(s) for the multiplicative forecast calculated using ETS or EDS algorithms for the given arguments.

## Arguments:

**target** is a date, time, or numeric single value or range. The data point/range for which to calculate a forecast.

**values** is a numeric array or range. **values** are the historical values, for which you want to forecast the next points.

**timeline** is a real number or dates or time array or a reference to the range to cells containing them. The timeline (x-value) range for historical values.

**confidence_level** is a numeric value between 0 and 1 (exclusive), default is 0.95. A value indicating a confidence level for the calculated prediction interval.

**period_length** is a numeric value >= 0, the default is 1. A positive integer indicating the number of samples in a period.

**data_completion** is a logical value TRUE or FALSE, a numeric 1 or 0, default is 1 (TRUE). A value of 0 (FALSE) will add missing data points with zero as historical value. A value of 1 (TRUE) will add missing data points by interpolating between the neighboring data points.

**aggregation** is a numeric value from 1 to 7, with default 1. The aggregation parameter indicates which method will be used to aggregate identical time values:

Aggregation | Function |
---|---|

1 | AVERAGE |

2 | COUNT |

3 | COUNTA |

4 | MAX |

5 | MEDIAN |

6 | MIN |

7 | SUM |

For example, with a 90% Confidence level, a 90% prediction interval will be computed (90% of future points are to fall within this radius from forecast).

For ETS, Calc uses an approximation based on 1000 calculations with random variations within the standard deviation of the observation data set (the historical values).

- If a constant step can't be identified in the sorted
**timeline**, the function will return a numeric(#NUM!) error. - If the ranges of the
**timeline**and historical**values**aren't of the same size, the function will return an error value. - If the
**timeline**contains less than 2 periods of data, the function will return a value(#VALUE!) Error. - If
**confidence_level**values are <= 0 or >= 1, the function will return the #NUM! Error. - For values of
**period_length**that not being a positive whole number, the function will return a numeric(#NUM!) Error.

## Additional details:

- Exponential Smoothing is a method to smooth real values in time series in order to forecast probable future values.
- Exponential Triple Smoothing (ETS) is a set of algorithms in which both trend and periodical (seasonal) influences are processed. Exponential Double Smoothing (EDS) is an algorithm like ETS, but without the periodical influences. EDS produces linear forecasts.
- FORECAST.ETS.PI.MULT calculates with the model:

- For more details on Exponential smoothing algorithms, visit Wikipedia.

## Examples:

The table below contains a timeline and its associated values:

A | B | |
---|---|---|

1 | Timeline | Values |

2 | 01/01/2013 | 112 |

3 | 01/02/2013 | 118 |

4 | 01/03/2013 | 132 |

5 | 01/04/2013 | 100 |

6 | 01/05/2013 | 121 |

7 | 01/06/2013 | 135 |

8 | 01/07/2013 | 148 |

9 | 01/08/2013 | 148 |

10 | 01/09/2013 | 136 |

11 | 01/10/2013 | 119 |

12 | 01/11/2013 | 104 |

13 | 01/12/2013 | 118 |

Formula | Description | Returns |
---|---|---|

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.9;1;TRUE();1) with Values and Timeline as the named ranges from the table above | The prediction interval for multiplicative forecast for January 2014 based on Values and Timeline named ranges above, confidence level of 90% (=0.9) with one sample per period, no missing data, and AVERAGE as aggregation. |
19.8123814943636 |

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.8;4;TRUE();7) with Values and Timeline as the named ranges from the table above | The prediction interval for multiplicative forecast for January 2014 based on Values and Timeline named ranges above, with confidence level of 0.8, period length of 4, no missing data, and SUM as aggregation. |
23.0920520833224 |

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.8;4;5;7) with Values and Timeline as the named ranges from the table above | The function returns an error value since data_completion cannot be anything except 0,FALSE,1 or TRUE. |
Err:502 |

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.8;1.5;TRUE();7) with Values and Timeline as the named ranges from the table above | The function returns a numeric error since period_length is not a positive whole number. |
#NUM! |

## Related LibreOffice functions:

## ODF standard:

None

## Equivalent Excel functions:

None