Question

1Year Sales (in $1000s) 283 288 336 388 406 412 416 435 428 435 462 452 474 476 497 487 523 528 532 552 4 4 6 6 9 10 11 10 12 11 13 12 14 13 1514 16 15 17 16 18 17 19 18 20 19 21 20 23 24

Answer 1

a.

   The data is stationary at trend and intercept because the graph follows the positive trend without any break.

b.
Year   Sales   MV   Forecast   Error   MSE
1   283              
2   288   285.5          
3   336   312   285.5   50.5   2550.25
4   388   362   312   76   5776
5   406   397   362   44   1936
6   412   409   397   15   225
7   416   414   409   7   49
8   435   425.5   414   21   441
9   428   431.5   425.5   2.5   6.25
10   435   431.5   431.5   3.5   12.25
11   462   448.5   431.5   30.5   930.25
12   452   457   448.5   3.5   12.25
13   474   463   457   17   289
14   476   475   463   13   169
15   497   486.5   475   22   484
16   487   492   486.5   0.5   0.25
17   523   505   492   31   961
18   528   525.5   505   23   529
19   532   530   525.5   6.5   42.25
20   552   542   530   22   484
21           542       14896.75

MV denotes moving average = current sales + Previous year sales/ number of years = (283+288)/2 =285.5
Error =(Actual values – Forecasted Value)
N= denotes number of errors
MSE =( Summation of absolute value of error)^2 / number of years = 14896.75/18 = 827.5972

c. Last year moving average becomes this year forecasted value. Forecasted value for year 21 is 542

d
Year   Sales   MV   Forecast   Error
1   283          
2   288          
3   336          
4   388   323.75      
5   406   354.5   323.75   82.25
6   412   385.5   354.5   57.5
7   416   405.5   385.5   30.5
8   435   417.25   405.5   29.5
9   428   422.75   417.25   10.75
10   435   428.5   422.75   12.25
11   462   440   428.5   33.5
12   452   444.25   440   12
13   474   455.75   444.25   29.75
14   476   466   455.75   20.25
15   497   474.75   466   31
16   487   483.5   474.75   12.25
17   523   495.75   483.5   39.5
18   528   508.75   495.75   32.25
19   532   517.5   508.75   23.25
20   552   533.75   517.5   34.5
21           533.75  

MV denotes moving average = current sales + Previous year three year sales / number of years of moving average = (283+288+336+388)/4 = 323.75
Error =(Actual values – Forecasted Value)
N= denotes number of errors
MAD =( Summation of absolute value of error)/ number of years =491/16 = 30.6875

e. Last year moving average becomes this year forecasted value = 533.75