Answered: Consider the following time series…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	23	15	20	12	18	22	15

(a)	Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)

What type of pattern exists in the data?

(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?

(e)

Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE.

Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient.

α =

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