Trick=MBHsmooths1(982:996,3); % pad with instrumental (1981..1995) ..
out98t=flipud(filter(B98,A98,flipud([filter(B98,A98,[in98;Trick;zeros(100,1)])]))); %..then smooth
out98t=out98t(26:576); % out98t is the smoothed recon ( years 1425..1975 ) in 5b, isn’t it ?

load MBHsmooths1.txt

[B99,A99]=butter(10,2/40); % MBH99
[B98,A98]=butter(10,2/50); % MBH98

ini=isfinite(MBHsmooths1(:,2));
in99=MBHsmooths1(ini,2);
in98=in99(401:end);
out98=flipud(filter(B98,A98,flipud([filter(B98,A98,[in98;zeros(100,1)])])));
out98=out98(26:576);
out99=flipud(filter(B99,A99,flipud([filter(B99,A99,[in99;zeros(100,1)])])));
out99=out99(1:981);

Now I need to post the “trick” code, just a sec..

here’s the data
% Year AnnualRecon Instrumental MB98SmoothTrick MBH98SmoothNoTrick MBH99SmoothTrick MBH99SmoothNoTrick
http://www.climateaudit.info/wp-content/uploads/2009/11/mbhsmooths1.txt

I’ll clean & post the code, just a minute

It doesn’t help that the original MBH98 5b (the black in your graph) is very hard to read to start with, being in B&W with too many lines at once, even though other figures in the same article are in color. It would be a lot easier to study the smoothing if the standard error lines were omitted, and if the smoothed reconstruction were a heavy solid line rather than a heavy broken line.

But then, what is your green line? Since you say the red line is “zero padded 5b smooth”, does this make the green line “instrumental (81-95) padded 5b smooth”? But this looks backwards — zero is below the end of the reconstruction, while the 81-95 instrumental data is higher, yet the green line is diving towards zero while the red line is climbing in the last two decades (except, inexplicably, the last few years).

Then, is one of these supposed to look like the MBH smoothed reconstruction at the end? I don’t see its last few broken segments in your graph at all.

It’s clear that the trick of splicing instrumental data onto a reconstruction before smoothing and then identifying the product as a smoothed reconstruction has been used several times by Jones et al. But this MBH98 5b is where the original Mike’s Nature Trick would be.

(I’d agree with Tim Lambert that MBH98 fig. 7 merely plots the two on the same graph as separate lines, and is not splicing them together as if they were one. I’ll mention this over at http://climateaudit.org/2007/05/11/the-maestro-of-mystery/)

Do you have the papers Thom (1954) “THE RATIONAL RELATIONSHIP BETWEEN HEATING DEGREE DAYS AND TEMPERATURE” and Thom (1966) “NORMAL DEGREE DAYS ABOVE ANY BASE BY THE UNIVERSAL TRUNCATION COEFFICIENT”?

I just got them and they seem to have the very basic statistical model used to calculate monthly station temperature means that Jones implicitly assumes in all his papers, and that forms the basis for the USHCN series. If you don’t have them, and would like pdf copies, drop me a line by email.

Pat

This is what it produced:

http://i27.tinypic.com/309pt02.gif

It also claimed a verification R2 of 0.998 for the 1400AD step …

… just kidding

Indeed, there is assumption of no serial correlation, but errors can be correlated between responses. Yet, this correlation is to be estimated (after computing ) so it cannot be used before.

CCE is not ML estimator, Sunberg99:

The classical estimator is not ML (unless q=p). Heuristically this is because only p-vector part of the q-vector is used for estimation of the unknown x, and the remaining q-p components contain some (little) information about

Brown87: Confidence and Conflict in Multivariate Calibration, Philip J. Brown; Rolf Sundberg; Journal of the Royal Statistical Society. Series B (Methodological), Vol. 49, No. 1. (1987), pp. 46-57.