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- From: len@mel.dit.csiro.au (Len Makin)
- Newsgroups: sci.math.stat
- Subject: Time series de-trend and df
- Message-ID: <1992Dec21.013932.24703@mel.dit.csiro.au>
- Date: 21 Dec 92 01:39:32 GMT
- Sender: news@mel.dit.csiro.au
- Organization: CSIRO DIT (Melb.)
- Lines: 35
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- A Climate modeller colleague asked the following:
- I am planning to remove trend from some GCM results (CO2 levels).
- I suspect this affects degrees of freedom for t-tests, F-tests, etc.
- Can anyone help please?
- I plan to remove the trend without changing the mean.
- I suspect not changing mean implies that only one df is lost.
-
- So if original data are
- y[1], y[2], ... , y[i], ... , y[N]
- where i represents year, so data are equally spaced in time.
-
- Detrended value for year i is:
- y[i] - r(y,i) * ( sd(y) / sd(i) ) * ( i - mean(i) )
-
- where r(y,i) is correlation between y & i
- r(y,i) = ( sum(i*y[i]) - mean(i) * mean(y) ) / ( sd(i) * sd(y) )
-
- Since i is simply 1, 2, ... , N
- by algebra:
- mean(i) = ( N + 1 ) / 2
- sd(i) = sqrt( ( N * N - 1 ) / 12 )
-
- In my case N = 20 for both control (normal CO2) & double CO2 samples.
- I plan to detrend both samples before comparing
- (1) means using t-test
- (2) variances using F-test.
-
- What is the effect of this detrending on degrees of freedom for these tests?
- Are these tests meaningful?
-
- Len.Makin@mel.dit.csiro.au | Senior Computer Scientist |
- CSIRO Division of Information Technology | Supercomputing Support Group |
- 723 Swanston Street, Carlton | Tel: +61 3 282 2622 |
- VIC 3053, Australia | Fax: +61 3 282 2600 |
-