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Consider the following time series data. Year Value 1 234 2 287 3 255 4 310 5 29

ID: 3264778 • Letter: C

Question

Consider the following time series data.

Year

Value

1

234

2

287

3

255

4

310

5

298

6

250

7

456

8

412

9

525

10

436

Using the naïve method (most recent value) as the forecast for the next year, compute the following measures of forecast accuracy.

Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for year 11?

Using the average of all the historical data as a forecast for the next year, compute the following measures of forecast accuracy.
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for year 11?

Using a three-year moving average the historical data as a forecast for the next year, compute the following measures of forecast accuracy.
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for year 11?

Use = 0.2 to compute the exponential smoothing values for the time series.

Mean absolute error

Mean squared error

Mean absolute percentage error

What is the forecast for year 11?

Explain which method you would use and why?

Year

Value

1

234

2

287

3

255

4

310

5

298

6

250

7

456

8

412

9

525

10

436

Explanation / Answer

I think 3-year moving average is best as its MSE is lowest.

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3-year Exponential 1-year all-average 1 234 234 2 287 234 53 2809 18.466899 234 53 2809 18.466899 234 53 2809 18.466899 3 255 244.6 10.4 108.16 4.07843137 287 32 1024 12.54902 260.5 5.5 30.25 2.15686275 4 310 258.6666667 51.33333333 2635.11111 16.55913978 246.68 63.32 4009.4224 20.4258065 255 55 3025 17.741935 258.6666667 51.33333 2635.11111 16.5591398 5 298 284 14 196 4.697986577 259.344 38.656 1494.286336 12.9718121 310 12 144 4.0268456 271.5 26.5 702.25 8.89261745 6 250 287.6666667 37.66666667 1418.77778 15.06666667 267.0752 17.0752 291.562455 6.83008 298 48 2304 19.2 276.8 26.8 718.24 10.72 7 456 286 170 28900 37.28070175 263.66016 192.33984 36994.61405 42.1797895 250 206 42436 45.175439 272.3333333 183.6667 33733.4444 40.2777778 8 412 334.6666667 77.33333333 5980.44444 18.77022654 302.128128 109.871872 12071.82826 26.6679301 456 44 1936 10.679612 298.5714286 113.4286 12866.0408 27.5312067 9 525 372.6666667 152.3333333 23205.4444 29.01587302 324.102502 200.897498 40359.80454 38.26619 412 113 12769 21.52381 312.75 212.25 45050.0625 40.4285714 10 436 464.3333333 28.33333333 802.777778 6.498470948 364.282002 71.7179981 5143.471249 16.4490821 525 89 7921 20.412844 336.3333333 99.66667 9933.44444 22.8593272 Forecast 457.6666667 457.6666667 209458.778 378.625602 378.625602 143357.3461 436 436 190096 346.3 346.3 119923.69 MAE MSE MAPE MAE MSE MAPE MAE MSE MAPE 0 0 MAPE 75.85714286 63138.5556 18.26986647 84.1420453 103282.1493 20.7040023 72.444444 74368 18.864045 85.79392 108477.843 20.8769336