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Autoregressive Model: Example

The Office Concept Corp. has acquired a number of

office units (in thousands of square feet) over the last 8

years. Develop the 2nd order Autoregressive models.

Year Units

98 4

99 3

00 2

01 302 2

03 2

04 4

05 6

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Autoregressive Model: Example

SolutionYear Yi Yi-1 Yi-298 4 --- ---

99 3 4 ---

00 2 3 4

01 3 2 3

02 2 3 2

03 2 2 3

04 4 2 2

05 6 4 2

Coefficients

Intercept 3,5

X Variable 1 0,8125

X Variable 2 -0,9375

Excel Output

21

9375,08125,05,3 ttt YYY

Develop the 2nd order

table

Use Excel to run a

regression model

n = 6!!!

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Autoregressive Model Example:

ForecastingUse the 2nd order model to forecast number of

units for 2006:

625,4

49375,068125,05,3

9375,08125,05,3200420052006

YYY

21 9375,08125,05,3 ttt YYY

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Autoregressive Model Example:

ForecastingUse the 2nd order model to forecast number of

units for 2008:

??

625,49375,0??8125,05,3

9375,08125,05,3200620072008

YYY

CHAIN FORECAST

21 9375,08125,05,3 ttt YYY

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Autoregressive Model Example:

ForecastingIf we want to forecast number of units for 2008,

first we need to forecast the number of units for

2007:

633,169375,06245,48125,05,3

9375,08125,05,3200520062007

YYY

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Autoregressive Model Example:

ForecastingNow we can forecast number of units for 2008:

491,0

625,49375,0633,18125,05,3

9375,08125,05,3200620072008

YYY

21 9375,08125,05,3 ttt YYY

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Autoregressive Model Example:

Mean Forecast Error

625,4

633,1

1

3125,00625,01

0625,03125,01

115,5

]625,4633,11[1e

SMFE

3318,245,249,1 MFE

Lets construct the forecast interval for 2008.

We need MFE:

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Autoregressive Model Example:

Confidence Interval for Forecast

1}{ ,2008,2008 2008 MFEtYEMFEtYP knYkn

182,336;05,0, tt kn

05,01}3318,2182,3491,03318,2182,3491,0{2008

Y

EP

95,0}9108,79288,6{2008

Y

EP

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Why?

B1 or B2 can be statistically insignificant

Determination coefficient too low

Improper autoregression rank (p2)