R help - Jan 2004 - How can I test if time series residuals' are uncorrelated ?

Ok I made Jarque-Bera test to the residuals (merv.reg$residual)

library(tseries)
jarque.bera.test(merv.reg$residual)
X-squared = 1772.369, df = 2, p-value = < 2.2e-16
And I reject the null hypotesis (H0: merv.reg$residual are normally
distributed)

So I know that:
1 - merv.reg$residual aren't independently distributed (Box-Ljung test)
2 - merv.reg$residual aren't indentically distributed (Breusch-Pagan test)
3 - merv.reg$residual aren't normally distributed (Jarque-Bera test)

My questions is:
It is possible merv.reg$residual   be uncorrelated ?
cov[residual_t, residual_(t+k)] = 0 ?
Even when residuals  are not independent distributed !
(and we know that they aren't normally distributed and they aren't
indentically distributed )
And how can I tested it ?

Thanks.

> Hint, if a ts is normally distributed then independence and
uncorrelatedness
> are equivalent, hence you can test for normally distributed errors (e.g.
> Jarque-Bera-Test).
>
> HTH,
> Bernhard
>

	[[alternative HTML version deleted]]

Hi,

I tried to unsubscribe because this emailadress won't be valid anymore from 
next week on. I send a mail to r-help-requests at stat.math.ethz.ch 
with 'unsubscribe'in the body, and got the following reply:


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To:  kurt.sys at ugent.be 
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tnx,
Kurt.

>
> Ok I made Jarque-Bera test to the residuals (merv.reg$residual)
>
> library(tseries)
> jarque.bera.test(merv.reg$residual)
> X-squared = 1772.369, df = 2, p-value = < 2.2e-16
> And I reject the null hypotesis (H0: merv.reg$residual are normally
> distributed)
>
> So I know that:
> 1 - merv.reg$residual aren't independently distributed (Box-Ljung test)
> 2 - merv.reg$residual aren't indentically distributed (Breusch-Pagan
test)
> 3 - merv.reg$residual aren't normally distributed (Jarque-Bera test)
>
> My questions is:
> It is possible merv.reg$residual be uncorrelated ?
> cov[residual_t, residual_(t+k)] = 0 ?
> Even when residuals are not independent distributed !

Yes. E.g., in an ARCH(1) process, cov[y_t, y_(t+k) ] = 0 (k \neq 0), but 
cov[(y_t)^2, (y_(t+k))^2 ] \neq 0, hence no independence (and this is 
typical for financial time series).
>
> (and we know that they aren't normally distributed and they aren't
> indentically distributed )
> And how can I tested it ?
>
> Thanks.
>
>
>>> Hint, if a ts is normally distributed then independence and
>
> uncorrelatedness
>
>>> are equivalent, hence you can test for normally distributed errors
(e.g.
>>> Jarque-Bera-Test).
>>>
>>> HTH,
>>> Bernhard
>>>
>
>
>
> [[alternative HTML version deleted]]
>
Typically, financial time series exhibit fat tails, i.e., are not 
normally distributed (and in an ARCH setup, financial time series are 
usually not even conditionally normally distributed. The fat tails are 
fatter than what we would expect from the clustering of volatility).

best
Adrian

-- 
Dr. Adrian Trapletti
Trapletti Statistical Computing
Wildsbergstrasse 31, 8610 Uster
Switzerland
Phone & Fax : +41 (0) 1 994 5631
Mobile : +41 (0) 76 370 5631
Email : mailto:a.trapletti at bluewin.ch
WWW : http://trapletti.homelinux.com

>
>
>>
>> Ok I made Jarque-Bera test to the residuals (merv.reg$residual)
>>
>> library(tseries)
>> jarque.bera.test(merv.reg$residual)
>> X-squared = 1772.369, df = 2, p-value = < 2.2e-16
>> And I reject the null hypotesis (H0: merv.reg$residual are normally
>> distributed)
>>
>> So I know that:
>> 1 - merv.reg$residual aren't independently distributed (Box-Ljung
test)
>> 2 - merv.reg$residual aren't indentically distributed
(Breusch-Pagan
>> test)
>> 3 - merv.reg$residual aren't normally distributed (Jarque-Bera
test)
>>
>> My questions is:
>> It is possible merv.reg$residual be uncorrelated ?
>> cov[residual_t, residual_(t+k)] = 0 ?
>> Even when residuals are not independent distributed !
>
>
>
> Yes. E.g., in an ARCH(1) process, cov[y_t, y_(t+k) ] = 0 (k \neq 0), 
> but cov[(y_t)2, (y_(t+k))2 ] \neq 0,

The last equation should be autocov[y_t, y_(t+k)] \neq 0 or equivalently 
cov[(y_t)2, (y_(t+k))2 ] \neq (E[(y_t)2])2

best
Adrian

> hence no independence (and this is typical for financial time series).
>
>>
>> (and we know that they aren't normally distributed and they
aren't
>> indentically distributed )
>> And how can I tested it ?
>
>
>
>>
>> Thanks.
>>
>>
>>>> Hint, if a ts is normally distributed then independence and
>>>
>>
>> uncorrelatedness
>>
>>>> are equivalent, hence you can test for normally distributed
errors
>>>> (e.g.
>>>> Jarque-Bera-Test).
>>>>
>>>> HTH,
>>>> Bernhard
>>>>
>>
>>
>>
>> [[alternative HTML version deleted]]
>>
>
> Typically, financial time series exhibit fat tails, i.e., are not 
> normally distributed (and in an ARCH setup, financial time series are 
> usually not even conditionally normally distributed. The fat tails are 
> fatter than what we would expect from the clustering of volatility).
>
> best
> Adrian
>
> -- 
> Dr. Adrian Trapletti
> Trapletti Statistical Computing
> Wildsbergstrasse 31, 8610 Uster
> Switzerland
> Phone & Fax : +41 (0) 1 994 5631
> Mobile : +41 (0) 76 370 5631
> Email : mailto:a.trapletti at bluewin.ch
> WWW : http://trapletti.homelinux.com
>
>