Question

The worldwide sales of cars from 1981-1990 are shown in the table below. Given: α = 0.2 and β = 0.15 (Hint: Use XLMiner) Year Units sold in thousands 1981 888 1982 900 1983 1000 1984 1200 1985 1100 1986 1300 1987 1250 1988 1150 1989 1100 1990 1200 Using the double exponential smoothing, find the value of the root mean square error for the given data.

Answer 1

The value of the root mean square error is 159.2935.

Alpha	0.2
Beta	0.15
Data			Forecasts and Error Analysis
Period	Demand		Smoothed Forecast, Ft	Smoothed Trend, Tt	Forecast Including Trend, FITt	Error	Absolute	Squared	Abs Pct Err
Period 1	888		888		888	0	0	0	00.00%
Period 2	900		888	1.71E-14	888	12	12	144	01.33%
Period 3	1000		890.4			109.6	109.6	12012.16	10.96%
Period 4	1200		912.32			287.68	287.68	82759.78	23.97%
Period 5	1100		969.856			130.144	130.144	16937.46	11.83%
Period 6	1300		995.8848			304.1152	304.1152	92486.05	23.39%
Period 7	1250		1056.708			193.2922	193.2922	37361.86	15.46%
Period 8	1150		1095.366			54.63373	54.63373	2984.844	04.75%
Period 9	1100		1106.293			-6.29302	6.293018	39.60207	00.57%
Period 10	1200		1105.034			94.96559	94.96559	9018.463	0.079138
			Total			1180.138	1192.724	253744.2	100.19%
			Average			118.0138	119.2724	25374.42	10.02%
						Bias	MAD	MSE	MAPE
							SE	178.0956

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