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# FORECAST.ETS.PI.MULT function

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

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.

See the Wikipedia on Exponential smoothing algorithms for more information.

FORECAST.ETS.PI.MULT calculates with the model

forecast = ( basevalue + trend * ∆x ) * periodical_aberration.

### Syntax

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

target (mandatory): A date, time or numeric single value or range. The data point/range for which to calculate a forecast.

values (mandatory): A numeric array or range. values are the historical values, for which you want to forecast the next points.

timeline (mandatory): A numeric array or range. The timeline (x-value) range for the historical values.

The timeline does not have to be sorted, the functions will sort it for calculations.
The timeline values must have a consistent step between them.
If a constant step cannot be identified in the sorted timeline, the functions will return the #NUM! error.
If the ranges of both the timeline and the historical values are not the same size, the functions will return the #N/A error.
If the timeline contains fewer than 2 data periods, the functions will return the #VALUE! error.

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

With values <= 0 or >= 1, the functions will return the #NUM! Error.

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

A value of 1 indicates that Calc is to determine the number of samples in a period automatically.
A value of 0 indicates no periodic effects, a forecast is calculated with EDS algorithms.
For all other positive values, forecasts are calculated with ETS algorithms.
For values that not being a positive whole number, the functions will return the #NUM! Error.

data_completion (optional): 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.

Although the time line requires a constant step between data points, the function support up to 30% missing data points, and will add these data points.

aggregation (optional): 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

Although the time line requires a constant step between data points, the functions will aggregate multiple points which have the same time stamp.

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).

Note on prediction intervals: there is no exact mathematical way to calculate this for forecasts, there are various approximations. Prediction intervals tend to be increasingly 'over-optimistic' when increasing distance of the forecast-X from the observation data set.

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).

#### Example

The table below contains a timeline and its associated values:

| A | B
1 | Timeline | Values
--- | --- | ---
2 | 01/2013 | 112
3 | 02/2013 | 118
4 | 03/2013 | 132
5 | 04/2013 | 100
6 | 05/2013 | 121
7 | 06/2013 | 135
8 | 07/2013 | 148
9 | 08/2013 | 148
10 | 09/2013 | 136
11 | 10/2013 | 119
12 | 11/2013 | 104
13 | 12/2013 | 118

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.9;1;TRUE();1)

Returns 20.1040952101013, 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.

=FORECAST.ETS.PI.MULT(DATE(2014;1;1);Values;Timeline;0.8;4;TRUE();7)

Returns 27.5285874381574, 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.

#### Technical information

This function is available since LibreOfficeDev 5.2.

This function is NOT part of the Open Document Format for Office Applications (OpenDocument) Version 1.3. Part 4: Recalculated Formula (OpenFormula) Format standard. The name space is

ORG.LIBREOFFICE.FORECAST.ETS.PI.MULT

Related Topics

FORECAST.ETS.PI.MULT wiki page.

See also: FORECAST.ETS.ADD, FORECAST.ETS.MULT, FORECAST.ETS.STAT.ADD, FORECAST.ETS.STAT.MULT, FORECAST.ETS.PI.ADD, FORECAST.ETS.SEASONALITY, FORECAST, FORECAST.LINEAR