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What is Moving Average?

 What is Moving Average?

It is technique use to calculate the overall trend with the help of historical data. To calculate the moving average simply calculates the average of set of data with time period. There are 4 type of Moving Average that is:

·         Simple Moving Average

·         Cumulative Moving Average

·         Weighted Moving Average

·         Exponential Moving Average

Example: Find out the simple moving average of following year sales data of XYZ Company by using 3 moving years

Year

Sales (Rs.)

1

5259

2

6453

3

9845

4

4865

5

3212

6

9856

7

4578

8

5965

Solution:

Year

Sales (Rs.)

Moving Average (for 3 years)

Deviation

Absolute Deviation

Squared deviation

Absolute Percentage Error

1

5259

 

 

 

 

 

2

6453

 

 

 

 

 

3

9845

(5259+6453+9845)/3 =7185.67

2659.33

2659.33

7072054

0.27012

4

4865

(6453+9845+4865)/3 =7054.33

-2189.33

2189.33

4793180

0.450017

5

3212

(9845+4865+3212)/3 =5974

-2762.00

2762.00

7628644

0.8599

6

9856

(4865+3212+9856)/3 =5977.67

3878.33

3878.33

15041469

0.3935

7

4578

(3212+9856+4578)/3 =5882

-1304.00

1304.00

1700416

0.284841

8

5965

(9856+4578+5965)/3 =6799.67

-834.67

834.67

696668

0.139927

 

Total

 

 

13627.67

36932432

2.398305

 

Deviation = Actual sales-Forecast (Moving average)

Absolute deviation =Ignore minus sign

Squared deviation = Absolute deviation ^2

 MAD = Ʃ ǀ actual –forecast ǀ / n

=13627.67/6

=2271.28

MSE = Ʃ (forecast errors) 2 / n

=36932432/6

=6155405.33

MAPE = 100* Ʃ ǀ actual i –forecast i ǀ/actual i / n

=2.398/6

=0.3996

Example: Find out the next year forecasted sales by using weighted moving average with the help of given information

Year

Sales

2012

49

2013

45

2014

32

2015

25

2016

28

 The weights are 0.6, 0.2 and 0.2

Solution:

 

A

B

C

D

1

Year

Sales

Weighted Moving Average

Formula

2

2012

49

 

 

3

2013

45

 

 

4

2014

32

 

 

5

2015

25

38

0.6*B4+0.2*B3+0.2*B2

6

2016

28

30.4

0.6*B5+0.2*B4+0.2*B3

7

2017

30

28.2

0.6*B6+0.2*B5+0.2*B4

8

2018

21

28.6

0.6*B7+0.2*B6+0.2*B5

9

2019

 

24.2

0.6*B8+0.2*B7+0.2*B6

 Highest Weight is given to recent sales price and less weight is given to last year to calculate average.

Example: Find out the MAD and MSE of given information:

Year

Demand

2015

40

2016

35

2017

38

2018

42

2019

55

Weights are 0.5 and 0.3.

Solution:

 

A

B

C

D

E

F

1

Year

Demand

Weighted Moving Average

Formula

Deviation

Squared deviation

2

2015

40

 

 

 

 

3

2016

35

 

 

 

 

4

2017

38

14.75

(0.5*B3+0.3*B2)/2

23.25

540.56

5

2018

42

14.75

(0.5*B4+0.3*B3)/2

27.25

742.56

6

2019

55

16.2

(0.5*B5+0.3*B4)/2

38.8

1505.44

7

2020

59

20.05

(0.5*B6+0.3*B5)/2

38.95

1517.10

8

2021

37

23

(0.5*B7+0.3*B6)/2

14

196

 

Total

 

 

 

142.25

4501.67

 

MAD = Ʃ ǀ actual –forecast ǀ / n

=142.25/5

=28.45

MSE = Ʃ (forecast errors) 2 / n

= 4501.67/5

=900.34

Example: Find out the next month sales with the help information:

·         Using Exponential Moving Average

·         Sales of 6 months are given as

·         Alpha is 0.2

Month

Sales

EMA

Jan

88

38

Feb

98

?

March

94

?

April

75

?

May

86

?

June

80

?

 

Solution:

Month

Sales             

Exponential Moving Average

Jan

88

68

Feb

98

72

March

94

77.2

April

75

80.56

May

86

79.45

June

80

80.76

 

St=α*(Yt-1) + (1-α)*St-1

Where,

St= EMA

α= alpha*

(Yt-1) = Sales of previous period

St-1 = EMA previous period

S Feb = 0.2*88 + (1-0.2)*68

= 17.6+0.8*68

=17.6+54.4

Feb=72

=0.2*98+ (1-0.2)*72

=19.6 + 0.8*72

= 19.6 + 57.6

March=77.2

=0.2*94+ (1-0.2)*77.2

= 18.8 + 0.8*77.2

= 18.8 + 61.76

April=80.56

=0.2*75+ (1-0.2)*80.56

=15 + 64.45

May=79.45

=0.2*86 + (1-0.2)*79.45

=17.2 + 63.56

June= 80.76

 

 

 

 

 

 

 

 

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