Develop a two-period weighted moving average forecast for March 2016 through Jan

ID: 425616 • Letter: D

Question

Develop a two-period weighted moving average forecast for March 2016 through January 2017. Use weights of 0.8 and 0.2, with the most recent observation weighted higher. Calculate the MFE, MAD, and MAPE values for March through December. E Click the icon to view the time series data. Develop a two-period weighted moving average and fill-in the table below (enter your responses rounded to one decimal place). Month Demand Forecast January 2016 February 95 94 81 95 132 109 114 90 93 86 92 March May June July August September 0 The forecast for January 2017 is 0 Enter your response rounded to one decimal place.) The MFE is ?. (Enter your response rounded to one decimal place and include a minus sign if necessary.) The MAD is O. (Entor your response rounded to one decimal placo.) The MAPE is 10 %. (Enter your response rounded to one decimal place.)

Explanation / Answer

Please refer below table for ready reference of relevant data :

Month

Demand

Forecast

Forecast error

Absolute deviation

Absolute Percentage error

January,2016

February

March

77.4

16.6

17.66

April

89.8

-8.8

8.8

10.86

May

83.6

11.4

12.00

June

132

92.2

39.8

30.15

July

109

124.6

-15.6

15.6

14.31

August

114

113.6

0.4

0.35

September

113

-23

25.56

October

94.8

-1.8

1.8

1.94

November

92.4

-6.4

6.4

7.44

December

87.4

4.6

5.00

SUM =

17.2

128.4

125.27

Following may be noted :

Ft = 0.8 x Dt-1 + 0.2 x Dt-2

Ft = Forecast for period t

Dt-1 , Dt-2 = Demands for period t-1 and t-2 respectively

Accordingly forecast for January 2017

= 0.8 x Demand for December 2016 + 0.2 x Demand for November, 2016

= 0.8 x 92 + 0.2 x 86

= 73.6 + 17.2

= 90.8

B ) Forecast error for period t = Demand for period t – Forecast for period t

Thus sum of all forecast errors ( total 10 months ) = 17.2

Therefore , Mean forecast error = Sum of forecast errors/ Number of data ( i.e 10 ) = 17.2/10 = 1.72

C) Absolute deviation for period t

= Absolute difference ( i.e non negative value ) between demand and forecast for period t

Thus sum of all Absolute deviations ( 10 observations ) = 128.4

Therefore, Mean absolute deviation ( MAD ) = 128.4/10 = 12.84

= Absolute deviation for period t/ Demand for period t x 100

Thus,

Sum of all Absolute Percentage error ( 10 observations ) = 125.27

Therefore . Mean absolute Percentage error ( MAPE ) = 125.27/10 = 12.527

THE FORECAST FOR JANUARY 20167 = 90.8

THE MFE IS = 1.72

THE MAD IS = 12.84

THE MAPE IS = 12.5