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

[Adrian Trapletti]

>
>
>>
>> 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
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>
>