1
$\begingroup$

I'm trying to understand property 1.1 below ($x_t$ is white noise), from Theorem A.7(also below).

From the formula for the $W$ matrix, using the more convenient one, I get $W_{pq}=0$ when $p\neq q$ and for $p=q$, $W_{pq}=\rho_x(0)^2=\sigma_x^4$. However, in property 1.1, I get $W_{pq}=1$.

So, where have I gone wrong?

Any help would be appreciated.

enter image description here

enter image description here

$\endgroup$
1
$\begingroup$

Well, I'm dyslexic a bit. Where I wrote autocovariance I should have written autocorrelation...

This is the problem... In property 1.1 we're dealing with the asymptotic distribution of the autoCORRELATION, not autocovariance. And the correlation of white noise is 1 for $p=q$ and 0 otherwise, which explains the asymptotic covariance of the autocorrelation estimator.

$\endgroup$
0
$\begingroup$

In theorem A.7, $\sigma_{\hat{p_x}(h)}^2 = \frac{W}{n}$ then for $n$ large, $\sigma_{\hat{p_x}(h)}^2 = \frac{W}{n} \approx \frac{1}{n}$

based on central limit theorem result $\sqrt{n} \; \hat{p_x} \xrightarrow{d} N(0,1) $, here's for details.

$\endgroup$
1
  • $\begingroup$ Kurnia, the pdf just states what I would like to prove... $\endgroup$ – An old man in the sea. Mar 22 '15 at 17:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.