TS module 15 MA(2) forecasting practice problems


TS module 15 MA(2) forecasting practice problems

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TS module 15 MA(2) forecasting practice problems

(The attached PDF file has better formatting.)

** Exercise 15.1: MA(2) parameters and forecasts

An MA(2) process has a mean

ì of 100 and the expected and actual values below in periods T-4 through T.

Period

Expected Value

Actual Value

T-4

100

100

T-3

100

100

T-2

100

101

T-1

100.2

101

T

99.8

99

What is the value of

è1?

What is the value of

è2?

What is the forecast for period T+1?

What is the forecast for period T+2?

Solution 15.1: Add residuals to the table and use periods T-1 and T to determine

è1 and è2.

Period

Expected Value

Actual Value

Residual

T-4

100

100

0

T-3

100

100

0

T-2

100

101

1

T-1

100.2

101

0.8

T

99.8

99

-0.8

Part A:

From the expected value in Period T-1 we solve for

è1:

100 –

è1 × 1 – è2 × 0 = 100.2 è1 = –0.2

Part B:

From the expected value in Period T and the value of

è1 we solve for è2:

100 –

è1 × 0.8 – è2 × 1 = 99.8 = 100 – 0.2

-0.2 × -0.8 –

è2 × 1 = –0.2

0.16 –

è2 = –0.2

è

2 = +0.36

Part C:

The forecast for period T+1 = 100 – (-0.8) × -0.2 – 0.8 × 0.36 = 99.552

Part D:

The fitted value in Period T+1 is the best estimate, so the expected residual is zero. The forecast for Period T+2 is

100 –

è2 × –0.8 = 100 – 0.36 × (–0.8) = 100.288

** Exercise 15.2: MA(2) process

An MA(2) process has a mean

ì of 100 and the expected and actual values below in periods T-4 through T.

Period

Expected Value

Actual Value

T-4

100

100

T-3

100

100

T-2

100

101

T-1

100.2

101

T

99.8

99

What is the forecast for period T+1?

What is the forecast for period T+2?

Part A:

Add residuals to the table and use periods T-1 and T to determine

ö1 and ö2.

Period

Expected Value

Actual Value

Residual

T-4

100

100

0

T-3

100

100

0

T-2

100

101

1

T-1

100.2

101

0.8

T

99.8

99

-0.8

Period T-1: 100 –

è1 × 1 – è2 × 0 = 100.2 è1 = –0.2

Period T: 100 –

è1 × 0.8 – è2 × 1 = 99.8 = 100 – 0.2

-0.2 × -0.8 –

è2 × 1 = –0.2

0.16 –

è2 = –0.2

è

2 = +0.36

The forecast for period T+1 = 100 + (-0.8) × -0.2 – 0.8 × 0.36 = 99.872

Part B:

For Period T+2, we assume the residual in Period T+1 is zero. The forecast for Period T+2 is

100 –

è2 × –0.8 = 100 – 0.36 × (–0.8) = 100.288


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apgarrity
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Exercise 15.2 Part B has a math error, should be 100-(-.8)x(-.2)-.36(.8), answer should be the same as in exercise 15.1?
ShubhankarYadav
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apgarrity - 12/3/2017 4:51:02 PM
Exercise 15.2 Part B has a math error, should be 100-(-.8)x(-.2)-.36(.8), answer should be the same as in exercise 15.1?


Yes, that is definitely a typo
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