Question

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

Date	A	B	C	D	Stock Exchange
9/3/10	127.37	18.34	21.03	15.51	10432.45
9/7/10	127.15	18.18	20.44	15.51	10334.67
9/8/10	124.92	17.88	20.57	15.82	10468.41
9/9/10	127.35	17.95	20.52	16.02	10498.61
9/10/10	128.37	17.82	20.42	15.98	10563.84
9/13/10	128.36	18.64	21.16	16.21	10616.07
9/14/10	128.61	18.83	21.29	16.22	10565.83
9/15/10	130.17	18.79	21.69	16.25	10627.97
9/16/10	130.34	19.16	21.76	16.36	10595.39
9/17/10	129.37	18.82	21.69	16.26	10517.99
9/20/10	130.97	19.12	21.75	16.41	10661.11
9/21/10	131.16	19.02	21.55	16.57	10687.95

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7). I was also able to calculate the MAD of each of the stocks:

MAD of Stock A = 1.32

MAD of Stock B = 0.37

MAD of Stock C = 0.41

MAD of Stock D = 0.26

MAD of Stock Exchange = 83.85

Help me to calculate the Mean Square Error (MSE) of the stocks.

Answer 1

s_o=x_o

Forcast (s_t)=0.3x+(1-0.3)s_t-1, t > 0

Square Error= (Actual value-forcast.)²

Date	A	B	C	D	Stock Exchange	Forecast					Square Error
9/3/2010	127.37	18.34	21.03	15.51	10432.45	A	B	C	D	Stock Exchange	A	B	C	D	Stock Exchange
9/7/2010	127.15	18.18	20.44	15.51	10334.67	127.3700	18.3400	21.0300	15.5100	10432.4500	0.0484	0.0256	0.3481	0.0000	9560.9284
9/8/2010	124.92	17.88	20.57	15.82	10468.41	127.3040	18.2920	20.8530	15.5100	10403.1160	5.6835	0.1697	0.0801	0.0961	4263.3064
9/9/2010	127.35	17.95	20.52	16.02	10498.61	126.5888	18.1684	20.7681	15.6030	10422.7042	0.5794	0.0477	0.0616	0.1739	5761.6905
9/10/2010	128.37	17.82	20.42	15.98	10563.84	126.8172	18.1029	20.6937	15.7281	10445.4759	2.4113	0.0800	0.0749	0.0635	14010.0507
9/13/2010	128.36	18.64	21.16	16.21	10616.07	127.2830	18.0180	20.6116	15.8037	10480.9852	1.1599	0.3869	0.3008	0.1651	18247.9145
9/14/2010	128.61	18.83	21.29	16.22	10565.83	127.6061	18.2046	20.7761	15.9256	10521.5106	1.0078	0.3911	0.2641	0.0867	1964.2083
9/15/2010	130.17	18.79	21.69	16.25	10627.97	127.9073	18.3922	20.9303	16.0139	10534.8064	5.1199	0.1582	0.5772	0.0557	8679.4513
9/16/2010	130.34	19.16	21.76	16.36	10595.39	128.5861	18.5116	21.1582	16.0847	10562.7555	3.0762	0.4205	0.3622	0.0758	1065.0106
9/17/2010	129.37	18.82	21.69	16.26	10517.99	129.1123	18.7061	21.3387	16.1673	10572.5458	0.0664	0.0130	0.1234	0.0086	2976.3407
9/20/2010	130.97	19.12	21.75	16.41	10661.11	129.1896	18.7403	21.4441	16.1951	10556.1791	3.1699	0.1442	0.0936	0.0462	11010.4949
9/21/2010	131.16	19.02	21.55	16.57	10687.95	129.7237	18.8542	21.5359	16.2596	10587.6584	2.0629	0.0275	0.0002	0.0964	10058.4118
								Sum of square error			24.3856	1.8644	2.2860	0.8679	87597.8081
										MSE	2.2169	0.1695	0.2078	0.0789	7963.4371

MAD of Stock A = 2.2169

MAD of Stock B = 0.1695

MAD of Stock C =0.2078

MAD of Stock D = 0.0789

MAD of Stock Exchange = 7963.4371