R help - Jan 2004 - How can I test if a not independently and not identically distributed time series residuals' are uncorrelated ?

I'm analizing the Argentina stock market (merv)
I  download  the data from yahoo

library(tseries)
Argentina <-
get.hist.quote(instrument="^MERV","1996-10-08","2003-11-03",
quote="Close")

merv <- na.remove(log(Argentina))

I made the Augmented Dickey-Fuller test to analyse
if merv have unit root:
adf.test(merv,k=13)
Dickey-Fuller = -1.4645, p-value = 0.805,
merv have unit root than diff(merv,1) is stationary.

Than I made Breushch-Pagan test to test if residuals are identically
distributed:
library(lmtest)
bptest(merv[2:1730]~-1+merv[1:1729],~merv[1:1729]+I(merv[1:1729])^2)
BP = 81.3443, df = 2, p-value = < 2.2e-16
So merv.reg$resid aren't identically distributed. Than merv is
heteroscedastik.

Finally I made  Box-Ljung test  to test if residuals are independently
distributed:
(H0: merv.reg$resid are independently distributed)
library(ts)
merv.reg <- lm(merv[2:1730]~-1+merv[1:1729])
Box.test(merv.reg$resid, lag=25,type="Ljung")
X-squared = 54.339, df = 25, p-value = 0.0006004
So, there is evidence to not reject the null hypothesis,
than the residuals are independently distributed.

Because the residuals are not independently distributed, we know that the
squares of residuals are correlated:
cov[(residuals_t)^2, (residuals_(t-k))^2] <> 0 (not zero for  k <>
0)

But, the residuals could be uncorrelated, (even when they 
are not independent distributed):
cov[residuals_t, residual_(t-k)]=0 !
How can I test that merv.reg$residuals are uncorrelated ?

Thanks a lot.


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I'm analizing the Argentina stock market (merv)
I  download  the data from yahoo

library(tseries)
Argentina <-
get.hist.quote(instrument="^MERV","1996-10-08","2003-11-03",
quote="Close")

merv <- na.remove(log(Argentina))

I made the Augmented Dickey-Fuller test to analyse
if merv have unit root:
adf.test(merv,k=13)
Dickey-Fuller = -1.4645, p-value = 0.805,
merv have unit root than diff(merv,1) is stationary.

Than I made Breushch-Pagan test to test if residuals are identically
distributed:
library(lmtest)
bptest(merv[2:1730]~-1+merv[1:1729],~merv[1:1729]+I(merv[1:1729])^2)
BP = 81.3443, df = 2, p-value = < 2.2e-16
So merv.reg$resid aren't identically distributed. Than merv is
heteroscedastik.

Finally I made  Box-Ljung test  to test if residuals are independently
distributed:
(H0: merv.reg$resid are independently distributed)
library(ts)
merv.reg <- lm(merv[2:1730]~-1+merv[1:1729])
Box.test(merv.reg$resid, lag=25,type="Ljung")
X-squared = 54.339, df = 25, p-value = 0.0006004
So, there is evidence to not reject the null hypothesis,
than the residuals are independently distributed.

Because the residuals are not independently distributed, we know that the
squares of residuals are correlated:
cov[(residuals_t)^2, (residuals_(t-k))^2] <> 0 (not zero for  k <>
0)

But, the residuals could be uncorrelated, (even when they 
are not independent distributed):
cov[residuals_t, residual_(t-k)]=0 !
How can I test that merv.reg$residuals are uncorrelated ?

Thanks a lot.

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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
>
> >

>
>
>I'm analizing the Argentina stock market (merv)
>I  download  the data from yahoo
>
>library(tseries)
>Argentina <-
get.hist.quote(instrument="^MERV","1996-10-08","2003-11-03",
quote="Close")
>
>merv <- na.remove(log(Argentina))
>
>I made the Augmented Dickey-Fuller test to analyse
>if merv have unit root:
>adf.test(merv,k=13)
>Dickey-Fuller = -1.4645, p-value = 0.805,
>merv have unit root than diff(merv,1) is stationary.
>
>Than I made Breushch-Pagan test to test if residuals are identically
distributed:
>library(lmtest)
>bptest(merv[2:1730]~-1+merv[1:1729],~merv[1:1729]+I(merv[1:1729])2)
>BP = 81.3443, df = 2, p-value = < 2.2e-16
>So merv.reg$resid aren't identically distributed. Than merv is
heteroscedastik.
>
>Finally I made  Box-Ljung test  to test if residuals are independently
distributed:
>(H0: merv.reg$resid are independently distributed)
>library(ts)
>merv.reg <- lm(merv[2:1730]~-1+merv[1:1729])
>Box.test(merv.reg$resid, lag=25,type="Ljung")
>X-squared = 54.339, df = 25, p-value = 0.0006004
>So, there is evidence to not reject the null hypothesis,
>than the residuals are independently distributed.
>
Palhoto,

Box.test is a test, which tests for independence using the acf of a time 
series. That means the test is in fact a test for uncorrelatedness 
rather than independence. Applying Box.test to the squares of the 
residuals is testing for ARCH effects in the time series. With stock 
index data, usually the time series are uncorrelated, but show strong 
ARCH effects, ie., are not independent. Other tests for independence are 
bds.test and terasvirta.test from tseries. The former is a more general 
test for independence, the latter focuses on neglected non-linearity in 
the conditional mean (white.test is designed for the same, but I do not 
recommend it). With stock index data, usually the time series are not 
i.i.d. according to the bds.test due to ARCH effects. With 
terasvirta.test you find sometimes neglected non-linearity in the 
conditional mean. However, from my experience, this is often due to an 
exogenuous structural break and not due to endogenuous non-linearity in 
conditional mean.

best
Adrian
                   
>Because the residuals are not independently distributed, we know that the
>squares of residuals are correlated:
>cov[(residuals_t)2, (residuals_(t-k))2] <> 0 (not zero for  k <>
0)
>
>But, the residuals could be uncorrelated, (even when they 
>are not independent distributed):
>cov[residuals_t, residual_(t-k)]=0 !
>How can I test that merv.reg$residuals are uncorrelated ?
>
>Thanks a lot.
>
>
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>
-- 
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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