Question

1. The number of fishing rods selling each day is given below. Perform analyses of the time series to determine which model should be used for forecasting. (10 points) a. 3 day moving average analysis b. 4 day moving average analysis c. 3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 with w1 on the oldest data d. exponential smoothing analysis with a = 0.3. e. Which model provides a better fit of the data? f. Forecast day 13 sales of fishing rods using the model chosen in part (e). Day Rods sold 1 60 2 70 3 110 4 80 5 70 6 85 7 115 8 105 9 65 10 75 11 95 12 85

Answer 1

(a)

Let shows the value of current day t. So 3 -day moving average can be calcualted as follow:

Following table shows the 3-day moving averages and aboslue values of forcast errors:

Day	Rods Sold	Forecast, 3 days moving average	|e|
1	60
2	70
3	110
4	80	80	0
5	70	86.67	16.67
6	85	86.67	1.67
7	115	78.33	36.67
8	105	90	15
9	65	101.67	36.67
10	75	95	20
11	95	81.67	13.33
12	85	78.33	6.67
Total			146.68

(b)

Let shows the value of current day t. So 4 -day moving average can be calcualted as follow:

Following table shows the 4-day moving averages and aboslue values of forcast errors:

Day	Rods Sold	Forecast, 4 days moving average	|e|
1	60
2	70
3	110
4	80
5	70	80	10
6	85	82.5	2.5
7	115	86.25	28.75
8	105	87.5	17.5
9	65	93.75	28.75
10	75	92.5	17.5
11	95	90	5
12	85	85	0
Total			110

(c)

Weighted moving averages will be calculated as follows:

Following table shows the weighted moving averages:

Day	Rods Sold	Forecast, 3 days weighted moving average	|e|
1	60
2	70
3	110
4	80	88	8
5	70	87	17
6	85	81	4
7	115	79.5	35.5
8	105	97	8
9	65	104	39
10	75	87	12
11	95	78	17
12	85	83	2
Total			142.5

(d)

Let shows the actual value for day t and shows the forecasted value of day t. So exponential smoothing forecast formula is

Assuming forecast for day 2 is actual value of day 1.

Following table shows the exponential smoothing forecast:

Day	Rods Sold	Forecast, exponential smoothing	|e|
1	60
2	70	60	10
3	110	63	47
4	80	77.1	2.9
5	70	77.97	7.97
6	85	75.58	9.42
7	115	78.41	36.59
8	105	89.39	15.61
9	65	94.07	29.07
10	75	85.35	10.35
11	95	82.25	12.75
12	85	86.08	1.08
Total			125.74

(e)

MAD is smallest for 4-day moving average. So it is best fit the data.

(f)

Forcasted value of day 13 is