Interpret Minitab output of AR(1) model

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

Minitab was used to fit an AR(1) model to a stationary series. The following output was obtained:

FINAL ESTIMATE OF PARAMETERS

Type	Coef	SE Coef	T	P
AR 1	X	{sea}	2.18	0.034
Constant	Y	{sed}	-0.12	0.902
Mean	{me}	{mese}

Give any introductory information the student needs.

			Name	Type	Generated Value

me	integer	130
a	number	0.33
c	number	-12.00
fo1	rational	-270
afo2	number	-2
fo2	number	-2.00
fo3	number	86.44
per	integer	58
afo4	number	115.6252
sed	integer	100
u	integer	90
mese	integer	250
tol	integer	0
afo3	number	86.44
fo4	number	115.63
sea	number	0.15
fo	rational	-270

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(50..150#10)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

130

→ Used by:

afo2
afo3
afo4
fo
fo1

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part c) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Input the values of X and Y:

X= Gap 0. (to 2 decimal places).

Y= Gap 1. (to 2 decimal places).

Advice

From the table we have $\displaystyle \frac{X}{\var{sea}}=2.18$ .

Hence we find $X=\var{sea}\times 2.18=\var{a}$ to 2 decimal places.

Similarly we have $\displaystyle \frac{Y}{\var{sed}}=-0.12$

Hence we find $Y=\var{sed}\times -0.12=\var{c}$ to 2 decimal places.

The model is

$Y_t= \var{me}+\var{a}(Y_{t-1}-\var{me})+\epsilon_t.$

So $a=\var{me},\;\;b=\var{a},\;\;c=\var{me}$ .

Putting $Y_{\var{per+1}}=\var{fo1}$ we find:

$Y_{\var {per + 2}} = \var{me} + \var{a} (Y_{\var{per + 1}} -\var{me}) = \var{me} + \var{a} \times (\var{fo1} -\var{me}) = \var{fo2}$ to 2 decimal places.

Using this value to 2dps we have:

$Y_{\var {per + 3}} = \var{me} + \var{a} (Y_{\var{per + 2}} -\var{me}) = \var{me} + \var{a} \times (\var{fo2} -\var{me}) = \var{fo3}$ to 2 decimal places.

Finally using this last value we have:

$Y_{\var {per + 4}} = \var{me} + \var{a} (Y_{\var{per + 3}} -\var{me}) = \var{me} + \var{a} \times (\var{fo3} -\var{me}) = \var{fo4}$ to 2 decimal places.

In summary we have.

Forecast from period {per}:

Period	Forecast
{per+1}	{fo1}
{per+2}	{fo2}
{per+3}	{fo3}
{per+4}	{fo4}

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Interpret Minitab output of AR(1) model

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`