Question

In: Statistics and Probability

(a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place.

Consider the following time series data:
Month 1 2 3 4 5 6 7
Value 24 13 21 13 20 24 16

(a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation.

(b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place.

Solutions

Expert Solution

solution:

Given data

Month	1	2	3	4	5	6	7
Values	24	13	21	13	20	24	16

a) Calculating MSE using Most Recent Value (Naive method) Method

Naive Forecasting: Naive forecasting is a forecasting Technique which uses quantitative data for its data estimation.It is easy to forecast the next month data by simply putting the previous data of last month to next month.

Using naive method forecast for next month is;

Month	Value (A)	Forecast Naive Method (N)	Error (A-N)	Absolute Error \| (A-N) \|	Squared Absolute Error \|(A-N) \|^2
1	24
2	13	24	-11	11	121
3	21	13	8	8	64
4	13	21	-8	8	64
5	20	13	7	7	49
6	24	20	4	4	16
7	16	24	-8	8	64
		16	=-8	= 46	=378

Mean Squared Error (MSE) is Squared Absolute Error divided by No.of months forecasted

MSE = |(A-N) |^2 / 6

= 378/6

= 63

Forecast for Month 8 = 16

b) MSE using the average of all the data available as the forecast for the next period

In this methof we simply Forecast the next period values by finding mean of its previous values

Month	Value (A)	Forecast (N)	Error (A-N)	Absolute Error \| (A-N) \|	Squared Absolute Error \|(A-N) \|^2
1	24
2	13	24	-11	11	121
3	21	(24+13)/2 =18.5	2.5	2.5	6.25
4	13	(24+13+21)/3 =58/3	-19/3	19/3	361/9
5	20	(24+13+21+13)/4 =17.75	2.25	2.25	5.0625
6	24	(24+13+21+13+20)/5 =18.2	5.8	5.8	33.64
7	16	(24+13+21+13+20+24)/6 =115/6	-19/6	19/6	361/36
			=-597/60	= 1863/60	=777929/3600

Mean Squared Error (MSE) is Squared Absolute Error divided by No.of months forecasted

MSE = |(A-N) |^2 / 6

= (777929/3600) / 6

= 36.0

Forecast for Month 8 = (24+13+21+13+20+24+16) / 7 = ~18.7

a) MSE = 63

Forecast for Month-8 = 16

b) MSE = 36

Forecast for Month-8 = 18.7

orchestra answered 1 year ago

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