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