Question

Here are earnings per share for two companies by quarter from the first quarter of three years ago through the second quarter of this year. Forecast earnings per share for the rest of this year and next year. Use exponential smoothing to forecast the third period of this year, and the time series decomposition method to forecast the last two quarters of this year and all four quarters of next year. (It is much easier to solve this problem on a computer spreadsheet so you can see what is happening.) EARNINGS PER SHARE QUARTER COMPANY A COMPANY B 3 years ago I $ 1.63 $ 0.19 II 2.34 0.25 III 1.15 0.22 IV 1.19 0.31 2 years ago I 1.61 0.23 II 2.03 0.32 III 1.18 0.33 IV 0.26 0.44 last year I 0.26 0.36 II –0.22 (loss) 0.45 III –0.94 (loss) 0.46 IV 0.20 0.45 this year I –1.59 (loss) 0.28 II 0.33 0.45 a. For the exponential smoothing method, choose the first quarter of 3 years ago as the beginning forecast. Make two forecasts: one with α = 0.20 and one with α = 0.10. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) Calculate the MAD for each forecast using data starting with second quarter of 3 years ago through second quarter of this year. (Round your answers to 3 decimal places.) Using the MAD method of testing the forecasting model's performance, plus actual data from 3 years ago through the second quarter of this year, how well did the model perform? Using the decomposition of a time series method of forecasting, forecast earnings per share for the last two quarters of this year and all four quarters of next year. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

Answer 1

Formula underlying exponential smoothing method can be seen below:

F_t = F_t-1 + $\alpha$ x (A_t-1 - F_t-1)

where

F_t-1 = Forecast for the period before current time period t

A_t-1 = Actual value for the period before current time period t

$\alpha$ = Weight between 0 and 1

F_t = Forecast for the current time period t

I am attaching a screenshot of my excel below in "show formula mode". This will tell you the formula used in each cell:

Below this, please find the actual output.

		Alpha	0.20			0.10
			Forecast
Time	Period	EPS (Actual)	Forecast at Alpha = 0.20	D = Actual - Forecast	Squared deviation	Forecast at Alpha = 0.10	D = Actual - Forecast	Squared deviation
3 Years ago, Q1	1	1.63
3 Years ago, Q2	2	2.34	1.630	0.71	0.50	1.630	0.71	0.50
3 Years ago, Q3	3	1.15	1.772	(0.62)	0.39	1.701	(0.55)	0.30
3 Years ago, Q4	4	1.19	1.648	(0.46)	0.21	1.646	(0.46)	0.21
2 Years ago, Q1	5	1.61	1.556	0.05	0.00	1.600	0.01	0.00
2 Years ago, Q2	6	2.03	1.567	0.46	0.21	1.601	0.43	0.18
2 Years ago, Q3	7	1.18	1.659	(0.48)	0.23	1.644	(0.46)	0.22
2 Years ago, Q4	8	0.26	1.564	(1.30)	1.70	1.598	(1.34)	1.79
1 Years ago, Q1	9	0.26	1.303	(1.04)	1.09	1.464	(1.20)	1.45
1 Years ago, Q2	10	-0.22	1.094	(1.31)	1.73	1.344	(1.56)	2.44
1 Years ago, Q3	11	-0.94	0.831	(1.77)	3.14	1.187	(2.13)	4.53
1 Years ago, Q4	12	0.20	0.477	(0.28)	0.08	0.974	(0.77)	0.60
This year, Q1	13	-1.59	0.422	(2.01)	4.05	0.897	(2.49)	6.19
This year, Q2	14	0.33	0.019	0.31	0.10	0.648	(0.32)	0.10
This year, Q3	15		0.082			0.617
Mean				(0.60)	1.03		(0.78)	1.42

The forecast for Q3 of this year is shown in the table above. Forecast EPS for Q3 of this year = 0.082 and 0.617 or Alpha= 0.2 and 0.1 respectively (Please see the table above)

MAD = Mean absolute deviation = -0.60 and -0.78 for Alpha= 0.2 and 0.1 respectively (Please see the table above)

MSD = mean squared deviation = 1.03 and 1.42 for Alpha= 0.2 and 0.1 respectively (Please see the table above)

None of the forecasting techniques are accurate. Hence, it's very difficult to objectively comment on the performance of the forecast. However based on MAD and MSD, the forecasting model has done reasonably well in case of Alpha = 0.20. The forecast model with Alpha = 0.2 is better than that with Alpha = 0.10.

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Using the decomposition of a time series method of forecasting, forecast earnings per share for the last two quarters of this year and all four quarters of next year.

Please post this as a separate question.