Question

The accompanying data file contains 10 observations for t and y_t.


A 3-period moving average is plotted along with the actual series.

a. Comment on smoothing.

• The jagged graph represents the original series and the smoother graph represents its 3-period moving average.

• The smoother graph represents the original series and the jagged graph represents its 3-period moving average.

• We cannot tell which graph represents the original series and which its 3-period moving average.

b-1. Use the 3-period moving average to make in-sample forecasts. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

t	yt	yˆt
1	13
2	8
3	9
4	13
5	13
6	8
7	8
8	10
9	12
10	14
11

b-2. Compute the resulting MSE and MAD. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

c. Make a forecast for period 11. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

yˆt= ?????  

Answer 1

using minitab>stat>Time series>Moving average

we have

Moving Average for yt

Data yt
Length 10
NMissing 0

Moving Average

Length 3

Accuracy Measures

MAPE 27.6195
MAD 2.9524
MSE 9.9683

Time yt MA Predict Error
1 13 * * *
2 8 * * *
3 9 10.0000 * *
4 13 10.0000 10.0000 3.00000
5 13 11.6667 10.0000 3.00000
6 8 11.3333 11.6667 -3.66667
7 8 9.6667 11.3333 -3.33333
8 10 8.6667 9.6667 0.33333
9 12 10.0000 8.6667 3.33333
10 14 12.0000 10.0000 4.00000

Forecasts

Period Forecast Lower Upper
11 12 5.81190 18.1881

a ) The smoother graph represents the original series and the jagged graph represents its 3-period moving average.

b-2. the resulting MSE = 9.97

and MAD = 2.95
c. a forecast for period 11

yˆt= 12