Question

Problem 15-01 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	13	15	10	19	13

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.

1. Mean absolute error. Round your answer to one decimal place.
   
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2. Mean squared error. Round your answer to one decimal place.
   
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3. Mean absolute percentage error. Round your answer to two decimal places.
   
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4. What is the forecast for week 7? Round your answer to the nearest whole number.
   

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Answer 1

Under the naive method of forecasting last period's actual values are used as this period's forecast , therefore forecasted values would start from week 2

Errors can be calculated as, Error = Forecast-Actual

Week	Value	Forecast	Error	| Error |	Error2	Error %
1	18
2	13	18	5	5	25	38.46%
3	15	13	-2	2	4	13.33%
4	10	15	5	5	25	50%
5	19	10	-9	9	81	47.37%
6	13	19	6	6	36	46.15%
7

a) MAE = Sum of absolute errors/ Number of error values

= 5+2+5+9+6/5

= 27/5

= 5.4

b) MSE = Sum of squared errors/Number of error values

=171/5

= 34.2

Error% = |Error| /Actual × 100%

c) Mean absolute percentage error (MAPE) = Sum of percentage error/Number of error values

= 195.31/5

=39.062

d) In accordance with the naive method, 7^th year forecasted value will be equal to the actual value in year 6

Therefore, forecast for week 7 will be 13.