Question

The values of Alabama building contracts (in millions of dollars) for a 12-month period follow.

230  340  230  270  280  320  220  310  240  290  260  230

1. Choose the correct time series plot.
   

   (i)	Value (Millions of dollars) Month (t)
   (ii)	Value (Millions of dollars) Month (t)
   (iii)	Value (Millions of dollars) Month (t)
   (iv)	Value (Millions of dollars) Month (t)

   
   ________________
   
   What type of pattern exists in the data? ______________
   
     
   
2. Compare a three-month moving average forecast with an exponential smoothing forecast. Use  = 0.2. Which provides the better forecasts based on MSE? Do not round your intermediate calculations and round your final answers to two decimal places.
   

   	Moving average	Exponential smoothing
   MSE

   
   ______________
3. What is the forecast for the next month? Round your answer to the nearest whole number.
   
   ______ millions of dollars

Answer 1

a)

horizontal trend

b)for 3 month forecast:

		3 month
t	value	forecast	error	error^2
1	230
2	340
3	230
4	270	266.67	3.33	11.09
5	280	280.00	0.00	0.00
6	320	260.00	60.00	3600.00
7	220	290.00	70.00	4900.00
8	310	273.33	36.67	1344.69
9	240	283.33	43.33	1877.49
10	290	256.67	33.33	1110.89
11	260	280.00	20.00	400.00
12	230	263.33	33.33	1110.89
		total	300.00	14355.04
		average	33.333	1595.00

for 0.2 smoothing forecast:

		exponential smoothing
month	value	forecast		error^2
1	230
2	340	230.00		12100.00
3	230	252.00		484.00
4	270	247.60		501.76
5	280	252.08		779.53
6	320	257.66		3886.28
7	220	270.13		2513.02
8	310	260.10		2490.01
9	240	270.08		904.81
10	290	264.07		672.36
11	260	264.07		16.56
12	230	269.25		1540.56
		260.00	total	25888.89
			average	2353.54

MSE for moving average =1595.00

MSE for exponential smoothing forecast =2353.54

c)

since MSE for moving average is less , this will provide the best forecast

forecast for the next month=(290+260+230)/3 =260