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.
FORECAST.ETS.PI.MULT calculates with the model
forecast = ( basevalue + trend * ∆x ) * periodical_abberation.
This function is available since LibreOffice 5.2.
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 time line (xvalue) range for the historical values.
The time line doesn't have to to be sorted, the functions will sort it for calculations.
The time line values must have a consistent step between them.
If a constant step can't be identified in the sorted time line, the functions will return the #NUM! error.
If the ranges of the time line and historical values aren't of same size, the functions will return the #N/A error.
If the time line contains less than 2 periods of data, 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 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 neighbouring data points.
Although the time line requires a constant step between data points, the function supports 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 'overoptimistic' when increasing distance of the forecastX 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).
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.