Question

In: Economics

Starting in year 4 and going to year 12, forecast demand using a 3-year moving average.

Consider the following data:

Year 1 2 3 4 5 6 7 8 9 10 11

Demand 7 9 5 9 13 8 12 13 9 11 7

Starting in year 4 and going to year 12, forecast demand using a 3-year moving average.

(a): What is the predicted value for the next period (Year 12)?

(b): What is the MAD value for this forecast? Starting in year 4 and going to year 12, forecast demand using a 3-year weighted moving average with weights of .1, .3, and .6, using .6 for the most recent year. What is the predicted value for the next period (Year 12)?

(c): What is the predicted value for the next period (Year 12)?

(d): What is the MAD value for this forecast?

Solutions

Expert Solution

Answer

(a)

In order to predict the value for the next period that is 12 th year . As given we have to take 8 year mving average .

So starting fromyear 4 to 12 , we get

Demand in year 12 = sum of demand from year 4 till 11 / number of observations = 9+13+8+12+13+9+11+7 / 8 =82/8 = 10.25 or 10

hence the predicted value for year 12 is 10

(b)

Now calculating the Mean absolute deviation(MAD) we have , the formula

MAD = summation of (xi-x (bar ) / n)

where xi is the individual demand and x(bar is the mean) and n is the no. of observation

So, mean is equal to = 9+13+8+12+13+9+11+7 +10 / 9 = 10.22 or 10

Now constructing the table

xi xi- x(bar) mod ( xi-x bar)
9 9-10 = -1 1
13 13-10 =3 3
8 8-10=-2 2
12 12-10 2
13 13-10=3 3
9 9-10=-1 1
11 11-10=1 1
7 7-10=-3 3
10 10-10=0 0

MAD = (1+3+2+2+3+1+1+3+0)/ 9= 16/9 = 1.77 or 2 (approx)

(c)

So, using weighted moving average we use the formula

Predicted value = most recent period demand * weight assigned / sum of weights

Demand in year 12 = (9*0.1+11*0.3+7*0.6)/(0.1+0.3+0.6) = 8.4/1 =8.4

hence predicted value in year 12 using weighted moving average is 8.4

(d)

mean is equal to = 9+13+8+12+13+9+11+7 +8.4 / 9 =90.4/9 = 10.044 or 10

MAD =

xi xi- x(bar) mod ( xi-x bar)
9 9-10 = -1 1
13 13-10 =3 3
8 8-10=-2 2
12 12-10 2
13 13-10=3 3
9 9-10=-1 1
11 11-10=1 1
7 7-10=-3 3
8.4 8.4 -10 = -1.6 1.6

MAD = (1+3+2+2+3+1+1+3+1.6/9= 17.6/9=1.955 or 2 (approx)

hence MAD is same in both the cases

Rahul Sunny answered 2 years ago
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