Question

Consider the following time series data: Month 1 2 3 4 5 6 7 Value 23...

Consider the following time series data:

 Month 1 2 3 4 5 6 7 Value 23 13 21 13 19 21 17
 (a) Create a time series plot.
 What type of pattern exists in the data? - Select your answer -Positive trend patternHorizontal patternVertical patternNegative trend patternItem 2 (b) Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE: The forecast for month 8: (c) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE: The forecast for month 8: (d) Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE? - Select your answer -3-month moving averageexponential smoothingItem 7 (e) Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. If required, round your answer to two decimal places.

a)

Horizontal

b)

 month value forecast error error^2 1 23 2 13 3 21 4 13 19.00 -6.00 36.00 5 19 15.67 3.33 11.11 6 21 17.67 3.33 11.11 7 17 17.67 -0.67 0.44 total 58.67

MSE=14.67

forecast =19

c)

 month value forecast error error^2 1 23 2 13 23.00 -10.00 100.00 3 21 21.00 0.00 0.00 4 13 21.00 -8.00 64.00 5 19 19.40 -0.40 0.16 6 21 19.32 1.68 2.82 7 17 19.66 -2.66 7.05 total 174.04

MSE=29.01

forecast =19.13 (try 19.12 if this comes wrong)

d) three-month moving average forecast o provide the better forecast due to smaller MSE

e)

alpha =0.32