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date	2004.11.08.22.49.52;	author wmc;	state Exp;
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@<a href=random.phtml,v>random.phtml,v</a>

<h4>MBH/M&M on random data</h4>

...continued from the main page.

<p>

OK, the idea is that instead of using real proxies we'll use random data.
This has the advantage that we can make as many series as we like. It
has the disadvantage that the data may not look like the real series.

<p>
Code:
<p>
<ol>
<li><a href=make_inf.pro>make_inf.pro</a> - IDL code to generate the .inf (control) and .txt (fake proxy) files, prior to running:
<li><a href=mbh.f>mbh.f</a> - (f77 -o mbh.exe mbh.f) - fortran code, modified from MBH's code
<li><a href=mbh2-rand.pro>mbh2-rand.pro</a> - IDL code to plot the PC's
</ol>

Note on the IDL code: you probably don't have IDL. If you do have it, you can't run
my code anyway because it relies on various local routines. But if you want to, mail me, and I'll put them up. You should however be able to read the code and work out
what its doing. Probably.

<P>
Anyway: I ran the above stuff 4 times over, to generate 4 realisations. If I were
a stats whizz then I'd just prove the properties of the output, but its easier to
just run examples. Here are the 4 (click to see):
<ol>
<li><a href=pc1-4_1000_100_1.png>pic 1</a>
<li><a href=pc1-4_1000_100_2.png>pic 2</a>
<li><a href=pc1-4_1000_100_3.png>pic 3</a>
<li><a href=pc1-4_1000_100_4.png>pic 4</a>
</ol>

So... M&M do have a partial point: the PC1 shapes (PC1 is the one in black)
do tend to have a trend in 1900-on.
<p>
But... when we look at the associated eigenvalues, there is a problem 
(JA finds the same, and in fact found it first). When I do the MBH method
on true proxy data, eigenvalue 1 is 0.55 (1000-) or 0.38 (1400-),
and clearly larger than following values. When I do
it on random data, eigenvalue 1 is 0.03 or thereabouts, and indistinct 
from following values. I think that is important.
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