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Standard error of the ARIMA constant

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Samik R.

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Dec 24, 2009, 4:33:24 PM12/24/09
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I am trying to manually calculate the standard error of the constant in
an ARIMA model, if it is included. I have referred to Box and Jenkins
(1994) text, specially Section 7.2, but my understanding is that the
methods mentioned here calculates the variance-covariance matrix for the
ARIMA parameters only, not the constant. Tried searching on the
Internet, but couldn't find any theory. Software like Minitab, R etc.
calculate this, so I was wondering what is the way? I know R source code
is available, but it is borderline incomprehensible (without any
comments etc. - and would take a long time to understand the theory).
Can someone provide any pointer(s) on this topic?
Thanks.

(Cross posted to sci.stat.math & sci.stat.consult)

wolfgang

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Dec 25, 2009, 3:45:05 AM12/25/09
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Usually, the constant variable is included in the covariance matrix.
When you can estimate the parameter then you should be able to have it
in the COV matrix.
And then that should be very easy,
Wolfgang

Samik R.

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Dec 26, 2009, 4:11:08 PM12/26/09
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On 12/25/2009 1:45 AM, wolfgang wrote:
> On Dec 24, 10:33 pm, "Samik R."<sam...@gmail.com> wrote:
>> I am trying to manually calculate the standard error of the constant in
>> an ARIMA model, if it is included. I have referred to Box and Jenkins
>> (1994) text, specially Section 7.2, but my understanding is that the
>> methods mentioned here calculates the variance-covariance matrix for the
>> ARIMA parameters only, not the constant. Tried searching on the
>> Internet, but couldn't find any theory. Software like Minitab, R etc.
>> calculate this, so I was wondering what is the way? I know R source code
>> is available, but it is borderline incomprehensible (without any
>> comments etc. - and would take a long time to understand the theory).
>> Can someone provide any pointer(s) on this topic?
>> Thanks.
>>
>> (Cross posted to sci.stat.math& sci.stat.consult)

>
> Usually, the constant variable is included in the covariance matrix.
> When you can estimate the parameter then you should be able to have it
> in the COV matrix.
> And then that should be very easy,
> Wolfgang

Thanks for your response. If the constant has to be included, I
generally transform the given data set by subtracting the mean out,
i.e., w_t = z_t - \mu, and then find out the ARMA parameters. Then I
calculate the constant using C = 1- \mu*(1 - Sum_{AR params})
I think the Box-Jenkins section talks about this same procedure, and in
this case, the constant is not included in the var-covar matrix. Isn't
this approach correct?
How would I go about including the constant in the var-covar matrix?

David Jones

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Jan 4, 2010, 9:29:22 AM1/4/10
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Have you tried a modernish book such as:

Harvey AC (1994) "Forecasting, structural time series models and the Kalman filter" , Cambridge University Press ISBN 0-521-40573-4

...this provides a computational procedure that does not subtract out the mean initially.

David Jones

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