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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.

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.

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 | دوال
--- | ---
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.

stat_type (mandatory): A numerical value from 1 to 9. A value indicating which statistic will be returned for the given values and x-range.

The following statistics can be returned:

stat_type | Statistics
--- | ---
1 | Alpha smoothing parameter of ETS algorithm (base)
2 | Gamma smoothing parameter of ETS algorithm (trend)
3 | Beta smoothing parameter of ETS algorithm (periodic deviation)
4 | Mean absolute scaled error (MASE) - a measure of the accuracy of forecasts.
5 | Symmetric mean absolute percentage error (SMAPE) - an accuracy measure based on percentage errors.
6 | Mean absolute error (MAE) – a measure of the accuracy of forecasts.
7 | Root mean squared error (RMSE) - a measure of the differences between predicted and observed values.
8 | Step size detected time line (x-range). When a stepsize in months/quarters/years is detected, the stepsize is in months, otherwise the stepsize is in days in case of date(time) timeline and numeric in other cases.
9 | Number of samples in period – this is the same as argument period_length, or the calculated number in case of argument period_length being 1.

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.

forecast = basevalue + trend * ∆x + periodical_aberration.

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

#### Example

The table below contains a timeline and its associated values:

| A | B
1 | Timeline | قيمة
--- | --- | ---
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