Question

Problem 1 (20 points) Daily high temperatures in Chicago for the past week were as follows 32, 37,50, 17, 23, 23, and 34 (yesterday). a) Forecast the high temperature today, using a 3-day moving average b) Forecast the high temperature today, using a 2-day moving average c) Calculate the mean absolute deviation based on a 2-day moving average d) Calculate the mean square error for the 2-day moving average e) Calculate the mean absolute percent error for the 2-day moving average.

Answer 1

The table summarize the forecasting methods and error measurements:

Day	Temperature (A)	3-day moving	2-day moving (F)	Error E = A - F	Absolute Deviation AD = |E|	Square Error SE = E2	Absolute % error %AE = (|E|) / A
1	32
2	37
3	50		(32+37)/2 = 31.71	(50 – 31.71) = 18.29	|18.29| = 18.29	(18.29)2 = 334.37	18.29/50 = 36.57%
4	17	39.67	(50+37)/2 = 31.67	-14.67	14.67	215.11	86.27%
5	23	34.67	30.60	-7.60	7.60	57.76	33.04%
6	29	30.00	25.75	3.25	3.25	10.56	11.21%
7	34	23.00	28.67	5.33	5.33	28.44	15.69%
Today		(34+29+23)/3 = 28.67	31.50
			Total	4.60	49.14	646.25	183%
			Average	0.92	9.83	129.25	37%

3-day moving average method: Forecast for period t = average of recent 3 day temperature

Today’s forecast = F₈ = (34 + 29 + 23)/3 = 28.67 units

2-day moving average method: Forecast for period t = average of recent 2 day temperature

Today’s forecast = F₈ = (34 + 29)/2 = 31.50 units

c.

First calculate 2-day moving from day 3 to 7. Calculate absolute deviation as follows from day 3 to 7:

Absolute deviation = | actual – Forecast |

Determine average absolute deviation by averaging absolute deviation from day 3 to 7.

Mean Absolute deviation (MAD) = 9.83

d.

First calculate 2-day moving from day 3 to 7. Calculate square error from day 3 to 7:

Squared error = (actual – Forecast)²

Determine average square error by averaging square error from day 3 to 7.

Mean Square Error (MSE) = 129.25

e.

First calculate 2-day moving from day 3 to 7. Calculate percentage absolute error from day 3 to 7 as follows:

% absolute error = |actual – Forecast| / Actual x 100

Determine Mean percentage absolute error (MPAE) by averaging % absolute error from day 3 to 7.

Mean % absolute error (MPAE) = 37%