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Consider the following time series data. Week 1 2 3 4 5 6 Value 20 13...

Consider the following time series data. Week 1 2 3 4 5 6 Value 20 13 15 11 17 14 Using the naïve method (most recent value)

Consider the following time series data. Week 1 2 3 4 5 6 Value 20 13 15 11 17 14 Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy: a. Mean absolute error (MAE) b. Mean squared error (MSE) c. Mean absolute percentage error (MAPE) Round your answers to two decimal places. MAE = MSE = MAPE = Using the average of all the historical data as a forecast for the next period, compute the same three values. Round your answers to two decimal places. MAE = MSE = MAPE = Which method appears to provide the more accurate forecasts for the historical data? Naïve method (most recent value) Average of all the historical data pt be graded, but may be reviewed and considered by your instructor.
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Question: Consider the following time series data.

Week 1 2 3 4 Value 20 13 15 11 17 14 5 6

Answer:

a. Using Naive method as the forecast for the next week, compute the following measures of forecat accuracy:

Naive Method: The naive forecast method is the simplest forecast method of all. The last period's actual value is taken as the current forecast value.

Overall calculation:

A B с F D Error E Error^2 1 Value Naïve Error% Week 1 20 2 3 13 20 7 49 53.85 N 4 3 15 13 2 4 5 4 11 15 4 16 13.33 36.36 35.2

Excel formulas:

A B E F C Naïve D Error Value Error 2 Error% 20 1 Week 2 1 3 2 4 3 13 =B2 =B3 5 4 15 11 17 =ABS(B3-C3) =ABS(B4-C4) =ABS(B5-C5

b. Using the average of all the historical data as a forecast for the next period, compute the same three values.

Overall calculation:

LL A Week B C D Value Avg. Data Avg. Data Error 20 E Error12 1 Error% 1 N 3 3 2 13 20 7 49 4 3 15 16.5 1.5 2.25 53.85 10.00 4

Excel formulas:

A B D E F с Avg. Data 1 Week Value Error Error 2 Error% 2 1 20 13 3 2 4 3 15 54 11 20 =ABS(B3-C3) =D3^2 =(B3+B2)/2 =ABS(B4-C4

c. Which method appears to provide the more accurate for the historical data?

Average of all the historical data, provides the better and accurate forecast in terms of MAE, MSE and MAPE when compared to the values of Naive method and its MAE, MSE and MAPE. Since, the error values are much lowest and more closest to the actual data.

Formulas for your reference:

Mean Absolute Error (MAE) = \sum |Error| / n

Here: |Error| = |Value - Forecast|

Mean Squared Error (MSE) = \sum Error^2 / n

Here: Error^2 = (Value - Forecast)^2

Mean Absolute Ppercentage Error (MAPE) = \sum Error% / n

Here: Error% = (|Error| / Value) x 100

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