Question

US Census Bureau tracks the median price for new home sales by month of year. The mediane price for April for the years 2001 to 2011 follow.

Years

Years	Price ($1000)
2001	175.2
2002	187.1
2003	189.5
2004	222.3
2005	236.3
2006	257.0
2007	242.5
2008	246.4
2009	219.2
2010	208.3
2011	224.7

a.         Compute a 2-week moving average for the above time series.

b.         Compute the mean square error (MSE) and mean Absolute deviation (MAD) for the

     2- year moving average forecast.

c.         Use a = 0.2 to compute the exponential smoothing values and MSE and MAD for

     the time series.

d. Which model is the best.? Justify your answer

e. Forecast the price for Year 2012.

Answer 1

a) 2- year moving average

	Years	Ft = Price ($1000)	2 MA	Error = Ft - 2 MA	ABS Error	Error^2	% ABS Error = ABS Error/Ft
	2001	175.2
	2002	187.1
	2003	189.5	181.15	8.35	8.35	69.7225	4.41%
	2004	222.3	188.3	34	34	1156	15.29%
	2005	236.3	205.9	30.4	30.4	924.16	12.87%
	2006	257	229.3	27.7	27.7	767.29	10.78%
	2007	242.5	246.65	-4.15	4.15	17.2225	1.71%
	2008	246.4	249.75	-3.35	3.35	11.2225	1.36%
	2009	219.2	244.45	-25.25	25.25	637.5625	11.52%
	2010	208.3	232.8	-24.5	24.5	600.25	11.76%
	2011	224.7	213.75	10.95	10.95	119.9025	4.87%
			216.5
Average					18.73889	478.1481	8.29%

b)

MAD = AVERAGE(ABS Error) = 18.7389

MSE = AVERAGE(Error^2) = 478.1481

MAPE = AVERAGE(% ABS Error) = 8.29%

c) Exponential smoothing

	Years	Ft = Price ($1000)	ES(0.2) = Ft-1 + α(At-1 - Ft-1)	Error = Ft - ES(0.2)	ABS Error	Error^2	% ABS Error = ABS Error/Ft
	2001	175.2	175.2	0	0	0	0
	2002	187.1	175.2	11.9	11.9	141.61	6.36%
	2003	189.5	177.58	11.92	11.92	142.0864	6.29%
	2004	222.3	179.964	42.336	42.336	1792.337	19.04%
	2005	236.3	188.4312	47.8688	47.8688	2291.422	20.26%
	2006	257	198.00496	58.99504	58.99504	3480.415	22.96%
	2007	242.5	209.803968	32.696032	32.69603	1069.031	13.48%
	2008	246.4	216.3431744	30.0568256	30.05683	903.4128	12.20%
	2009	219.2	222.3545395	-3.15453952	3.15454	9.95112	1.44%
	2010	208.3	221.7236316	-13.42363162	13.42363	180.1939	6.44%
	2011	224.7	219.0389053	5.661094707	5.661095	32.04799	2.52%
Average					23.45563	912.9551	10.09%

MAD = AVERAGE(ABS Error) = 23.4556

MSE = AVERAGE(Error^2) = 912.9551

MAPE = AVERAGE(% ABS Error) = 10.09%

d)

MAD for 2 MA < MAD for ES(0.2) and MSE also

2 MA is the best model to predict forecast

e)

the price for Year 2012 Forecast = 216.5