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9.2.1. Brown’s Exponential

This simply calculates the exponential weighted average in time. For a data series xt forecasts are given by:

   Time Series Analysis-Browns Exponential

where:

·      Time Series Analysis-Browns Exponential is the level at time t.

·      Time Series Analysis-Browns Exponential is the level smoothing constant.

 

Time Series Analysis-Browns Exponential

The initial value m0 is calculated as the average level in the first quarter of the series.

Time Series Analysis-Browns Exponential

Example

Open TIMESER and select Statistics 2Forecasting → Brown’s Exponential and select Wald Statistic

 (C2) as [Variable]. On the following dialogues accept the program’s sugestions:

Brown's Exponential

 

Level Smoothing Constant =

 0.2000

Sum of Squares =

 3029058.7929

 

Summary Table

Row

Cola Sales

Forecast

Lower 95%

Upper 95%

Level

1

 189.0000

 461.2000

*

*

 406.7600

2

 229.0000

 406.7600

-260.1178

 1073.6378

 371.2080

3

 249.0000

 371.2080

-179.9829

 922.3989

 346.7664

 …

34

 904.0000

 847.5220

 265.3873

 1429.6567

 858.8176

35

 715.0000

 858.8176

 289.7348

 1427.9004

 830.0541

36

 441.0000

 830.0541

 267.1638

 1392.9444

 752.2433

37

 

 752.2433

 178.5120

 1325.9746

 

38

 

 752.2433

 166.5580

 1337.9286

 

39

 

 752.2433

 153.6842

 1350.8023

 

 

 

46

 

 752.2433

 42.4548

 1462.0317

 

47

 

 752.2433

 24.1409

 1480.3456

 

48

 

 752.2433

 5.3481

 1499.1385

 

 

Time Series Analysis-Browns Exponential