# 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

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#### mathman

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

2 + ∑∑(k≠j) cov(k,j)

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

#### rhz

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

2 + ∑∑(k≠j) cov(k,j)

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

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