# Re: auto correlation Weatherhead et al. 1998

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
Date: Thu Jun 06 2013 - 13:45:45 MDT

I am not familiar with Weatherhead et al. (1998)

```--
how you can get values greater than (+,-) 1
http://www.ncl.ucar.edu/Document/Functions/Built-in/esacr.shtml
---
In short, 'qVar' is computed once using the entire series.
It uses all 't' values. Hence, it is a constant.
c(k) = SUM [(q(t)-qAve)*(q(t+k)-qAve)}]/qVar
Technically, at lag 'k' you have N-k values being used.
Then, you should calculate the standard deviation using
only the N-k values. This would result values always between -1 and +1.
However, using the standard deviation of the entire series results
in estimates that are asymptotically unbiased and consistent.
This is the pat chosen by NCL.
On 6/2/13 6:29 PM, Xin Xi wrote:
> Hello,
>
> I am using the method of Weatherhead et al. (1998) to test the significance
> of linear trends.I am in the step of computing the auto correlation
> coefficient at lag 1 of a 3D time series (lat x lon x time), which is the
> noise from detrending a dataset of same dimension. I used the esacr
> function and got values larger than 1, while the paper suggested the
> autocorrelation coeff should be in the [-1,+1] range. However the formula
> used in esacr seems to be right. Can anyone explain why? if you are
> familiar with the Weatherhead 1998 paper, is esacr the right function to
> use in this case?
>
> Thanks,
>
> Xin
>
>
>
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```
Received on Thu Jun 6 13:45:44 2013

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