[R] How can I test if time series residuals' are uncorrelated ?

[Adrian Trapletti]

Adrian Trapletti wrote:

>>
>>
>>>
>>> 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 

I don't know what I was thinking here, but it is a complete nonsense. My 
first remark (The line starting with "Yes.") was just correct.

best
Adrian