quick_tutorial.txt

替代数据法中最重要的文献和文献相关的软件代码

Basically, these are all very easy-to-use functions, if you know what you're
doing.  So, let's assume you read the Schreiber and Schmitz review paper on
surrogates.  This may not seem fair to you, but if so, I don't think this
collection of m-files is meant for you.  I'm just trying to help out fellow
researchers, who want to apply surrogate data to their own projects, by
sharing my own code.  I would also like to take this opportunity to ask all
researchers to make their code available (after publishing new methods,
naturally), so that people can try the algos and methods for themselves.
This would make life *so* much easier.  But enough of that, I'm starting to
sound like an old man, frustrated by decades of research, which, for the
record, I am not.

;P

I have included two functions to generate time series, one linear
> Xlin = generate_ar_signal ([.5 -.3 .3], 1000);
which generates a 1000-samples linear AR(3) signal with coeffs [.5 -.3 .3],
and one nonlinear
>> Xnl = generate_henon (1000);
which generates a realisation of the chaotic Henon Map.

Suppose we want to generate a surrogate (linearised version) of Xnl, using
the AR-method.  All we need to do is:
>> [Xs,MDL] = generate_AR (Xnl, 10);
where 10 is the maximal AR order to consider.  What this function does, is
fit progressively higher-order AR-models to the data, and penalises the
prediction error using the minimal description length.  This can be
visualised using the second output argument:
>> plot (MDL(:,1), MDL(:,2));
>> xlabel ('AR order'); ylabel ('MDL');

The other surrogate data generation methods for time series work in the same
way.  When only the first argument (the original time series) is provided,
the default parameters are used, which are usually just fine.  So,

>> Xs = generate_whatever_type_of_surrogate_time_series (Xnl);

will usually do the trick.  For a more detailed description of the
options, you can look at use the help function.  It is not my intention to
provide you with all the bits and pieces you need to understand everything
by itself: again, I'm assuming you've read Schreiber and Schmitz (2000).

Right, why do we need surrogate data?  Mostly to perform signal nonlinearity
analyses (other applications exist, though, and I've included some -> check
out the index.txt), so let's try that, using a nonlinearity statistic which 
measures the asymmetry due to time reversal, computed by comp_rev.m

>> Xnl = generate_henon (1000);
>> Tnl = comp_rev (Xnl);
>> n_surr = 24;		% Number of surrogates
>> Tnls = zeros(n_surr,1);
>> for n=1:n_surr, Xs = generate_iAAFT(Xnl);Tnls(n) = comp_rev(Xs);end
>> hist(Tnls),A=axis;line([Tnl Tnl], A(3:4));

So, now you can see the distribution of the test statistic under the
assumption of the null (Ts), and the vertical line denoting the value of the test
statistic for the original time series (To).  Clearly, To is not drawn from
this distribution, so you can safely conclude that Xnl is a nonlinear signal.
Trying the same for the linear signal,

>> Xlin = generate_ar_signal ([.5 -.3 .3], 1000);
>> Tlin = comp_rev (Xlin);
>> n_surr = 24;		% Number of surrogates
>> Tlins = zeros(n_surr,1);
>> for n=1:n_surr, Xs = generate_iAAFT(Xlin);Tlins(n) = comp_rev(Xs);end
>> hist(Tlins),A=axis;line([Tlin Tlin], A(3:4));

you'll see that the vertical line lies within the null distribution, so you
can conclude that Xlin is linear.

There exist several ways for statistically testing whether To is drawn
from Ts, and I have only implemented one of them (the easiest, which
also happens to be the one I always use): the rank-testing procedure.
Basically, [To;Ts(:)] is sorted in increasing order, and the rank index
for To is returned.  If this rank is unity or 25, this means that it
lies in the tail of the distribution, and the null can be rejected
(two-tailed test) with a significance of p=2*(1/(n_surr+1)).  So:
>> ranktest(Tnl,Tnls)
ans =
     1
%%%% Reject the null hypothesis of linearity
>> ranktest(Tlin,Tlins)
ans =
     5
%%%% Accept the null hypothesis of linearity
Increasing the number of surrogates (n_surr) will boost your confidence at
rejecting/accepting the null.

Well, that's about it.  I hope this bunch of code will help some people out.
For any suggestions/remarks, feel free to contact me:
[e-mail]
URL: http://134.58.34.50/temu