Sample standard deviation serially correlated normal data

[rhz]

Hi,

Can anyone point me to a reference for the statistical properties of the sample standard deviation of a sequence of identically distributed normal random variables subject to some form of serial correlation?

Thanks,

rhz

 

[mathman]

( ∑ X_k)² = ∑∑X_kX_j
Take expectation and subtract out the mean squared and you will have:

nσ² + ∑∑(k≠j) cov(k,j)

cov(k,j) is the covariance of X_kX_j.

 

[rhz]

( ∑ X_k)² = ∑∑X_kX_j
Take expectation and subtract out the mean squared and you will have:

nσ² + ∑∑(k≠j) cov(k,j)

cov(k,j) is the covariance of X_kX_j.

Hi,

OK, but I'm interested in the statistical properties of the sample standard deviation:

\sqrt{\hat\sigma^2} = \sqrt \left ( \frac{1}{N-1}\sum^{N-1}_{i=0}(x_i-\hat{\mu})^2 \right )
\hat\mu = \frac{1}{N}\sum^{N-1}_{i=0}x_i

Thanks.

 

[mathman]

Fix your latex!