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  • #361
  • Feb 14, 2009 9:12am Feb 14, 2009 9:12am
Quoting crodzilla
I have completed the implementation of a Goertzel "browser" on MT4. There are still some quirks I need to work out...

This is EURUSD 30m. The indicator shows all cycles sorted by amplitude for a specified period. Only the top cycle minus all other cycles is shown. As has been discussed before, there is a descent lead to the waveform.
Just to go on from my last post, Crodzilla's post #330 is quite encouraging!! It would be great to get a reasonably reliable LEADING indicator as he suggests might be possible.

CB
  • #362
  • Feb 14, 2009 11:08am Feb 14, 2009 11:08am
Quoting BarHopper
The difference in phase I was seeing last night was due to a minor error in the statement of the algorithm. In the mathcad diagram labeled "GX" the definition of the real and imaginary parts is incorrect. They should be:

real = s1 * XI - s2;
imag = s1 * sin(2 * pi * omega);

(Note that I'm using the original notation here: XI is the greek letter and I'm keeping omega even though it's often understood to mean 2 * pi * f)
Guys

The Devil is in the details..... I rather think that the two lines should correctly read:

real = (s1 * zeta) /2 - s2;
imag = s2 * sin(2 * pi * omega);

(The symbol used in the Matlab code is a Greek letter "zeta").

I am not on my Mathcad/Matlab machine at the moment so could be wrong but I think you will find the above is definitive... BarHopper, could you be as kind as to check this so we are all using the same (hopefully correct!) algorithm?

CB
  • #363
  • Feb 14, 2009 11:12am Feb 14, 2009 11:12am
...so this is what I am currently running with:

CB
Attached Image
  • #364
  • Edited 12:24pm Feb 14, 2009 12:00pm | Edited 12:24pm
Hi CB,

I just tried your revised equation for the Goertzel algorithm, and I get a significant disparity from the FFT. Perhaps we're using different definitions of loop counters or something? If you like, you can look at my Matlab code and see if I'm doing something wrong.

BTW, how are you deriving your equations? I derived mine by expanding the complex exponential in the Wikipedia equation using Euler's formula, and then collecting the real and imaginary terms.

Here's the code I'm using, with alternative definitions of the real and imaginary parts commented out. Feel free to experiment. Cheers...

Inserted Code
function [mag, phase] = bhGoertzel(x, f)
%
%   x: vector of length N containing timeseries on which to perform the 
%      spectral analysis
%
%   f: can be scalar or vector of arbitrary length M, containing 
%      target frequency(ies) measured in cycles per sample, 
%      on [0, 1/2] (Nyquist freq = 1/2)
%
%   mag: vector of length M>=1, with magnitude of DFT at points in f
%
% phase: vector of length M>=1, with phase of DFT at points in f
%

N = length(x);

cosine = 2 * cos(2 * pi * f);

s1 = zeros(size(f));
s2 = zeros(size(f));

for n=1:N
   s  = x(n) + s1.*cosine - s2;
   s2 = s1;
   s1 = s;
end

% from 1st Mathcad diagram - incorrect?
% realPart = s1 - (cosine .* s2) / 2;
% imagPart = s2 .* sin(2 * pi * f);

% My version - derived from wikipedia equations
% realPart = s1 .* cosine/2 - s2;
% imagPart = s1 .* sin(2 * pi * f);

% from revised Mathcad diagram - incorrect?
realPart = s1 .* (cosine/2) - s2;
imagPart = s2 .* sin(2 * pi * f);

mag = sqrt(realPart.^2 + imagPart.^2);

ix = realPart<0;  % logical index into phase, realPart, imagPart vectors
   phase(ix) = atan(imagPart(ix) ./ realPart(ix)) + pi;
ix = realPart>=0 & imagPart>=0;
   phase(ix) = atan(imagPart(ix) ./ realPart(ix));
ix = realPart>=0 & imagPart<0;
   phase(ix)  = atan(imagPart(ix) ./ realPart(ix)) + 2 * pi;
Attached Images
  • #365
  • Feb 14, 2009 5:54pm Feb 14, 2009 5:54pm
BarHopper

Many thanks for checking this, but I think we actually have the same equations. Is there just a bracket missing somewhere? Looking at your code and mine I think we are in agreement...

CB
  • #366
  • Feb 14, 2009 6:30pm Feb 14, 2009 6:30pm
Hi BarHopper

Just looking at your Matlab code now, I think we are in agreement.

Your Matlab code is:

N = length(x);
cosine = 2 * cos(2 * pi * f);
s1 = zeros(size(f));
s2 = zeros(size(f));
for n=1:N
s = x(n) + s1.*cosine - s2;
s2 = s1;
s1 = s;
end

realPart = s1 .* cosine/2 - s2;
imagPart = s1 .* sin(2 * pi * f);

mag = sqrt(realPart.^2 + imagPart.^2);

Which is what I think I have. Or am I misreading your code....

CB
  • #367
  • Feb 14, 2009 8:34pm Feb 14, 2009 8:34pm
Hi CB,

The only difference is that I have s1 in the imagPart where your 2nd mathcad diagram had s2. It was probably just a typo. Otherwise they are the same.

BTW, changing gears a bit... you seem to like the SSA algorithm... I've never used it, but it looks a bit like other algorithms I've seen in the past, in that it forms an estimate of a covariance matrix and uses SVD to find eigenvalues, etc. The main difference appears to be that it's aimed at scalar timeseries which leads to the embedding and subsequent diagonal averaging. I could see using it to filter out noise, do SNR estimation, or do prediction... What would you say it's best suited for?

Cheers...
  • #368
  • Feb 15, 2009 1:21am Feb 15, 2009 1:21am
Quoting BarHopper
Hi CB,

The only difference is that I have s1 in the imagPart where your 2nd mathcad diagram had s2. It was probably just a typo. Otherwise they are the same.

BTW, changing gears a bit... you seem to like the SSA algorithm... I've never used it, but it looks a bit like other algorithms I've seen in the past, in that it forms an estimate of a covariance matrix and uses SVD to find eigenvalues, etc. The main difference appears to be that it's aimed at scalar timeseries which leads to the embedding and subsequent diagonal averaging. I could see...

Guys

OK, BarHopper and I now agree on the code for Goertzel, so anyone wanting to implement can use either his Matlab of my MathCad code as a template.

On the SSA subject, I rather like SSA, particularly because it is DATA driven whereas nearly all other spectral algorithms (like FFT, Goertzel, MESA etc) are MODEL driven. There are no assumptions in SSA, it just decomposes time series into components and is very good at it.

Problem is, it needs an eigensolver like SVD which I wouldn't fancy implementing in MetaTrader! Of course, in Matlab it is a one-liner.

But like HP, SSA is non-causal (all the points are calculated from all the other points) so cannot be used directly for trading. But it certainly makes a good noise reducer.

I am attaching a Matlab routine to get you started if you want to have a play with it.

CB
Attached File(s)
File Type: zip SSA.zip   2 KB | 1,685 downloads
  • #369
  • Feb 15, 2009 3:01am Feb 15, 2009 3:01am
In the spirit of collaboration.......
Attached File(s)
File Type: ex4 SSA.ex4   2 KB | 1,414 downloads
File Type: zip ExpertSample.zip   4 KB | 1,323 downloads
  • #370
  • Feb 15, 2009 9:04am Feb 15, 2009 9:04am
Quoting anx
In the spirit of collaboration.......
Hi anx,

could you explain what the dll does? Is the .ex4 file indicator?

thanks

[Edit:] I guess it's an indicator that uses the dll to do SSA... haven't tested it though
  • #371
  • Feb 15, 2009 9:48am Feb 15, 2009 9:48am
Quoting challenger78
Hi anx,

could you explain what the dll does? Is the .ex4 file indicator?

thanks

[Edit:] I guess it's an indicator that uses the dll to do SSA... haven't tested it though


.dll file goes to libraries folder and .ex4 file goes to indicators folder
  • #372
  • Feb 15, 2009 10:06am Feb 15, 2009 10:06am
Hi CB, all,
Sorry to come back to this so late in the thread, but: 2 ways to link MT4 & Matlab: DDE & CSV.
What do you guys think of this FNN code (from Michael Small)? Looks good, right? (link) The problem that I have is to go from this, via Taken's theorem, to a number in minutes & seconds for the bin size of the charts. Care to explain a little more pls?

function =fnn(y,de,tau,th,kth);
if nargin<5,
kth=1;
disp(['th = ',int2str(kth)]);
end;
if nargin<4,
th=5;
disp(['th = ',int2str(th)]);
end;
if nargin<3,
tau=firstzero(y);
disp(['tau = ',int2str(tau)]);
end;
if nargin<2,
de=[1:10];
disp(['de = ',int2str(de(1)),':',int2str(de(end))]);
end;
p=[];
for t=tau,
px=[];
for d=de,
%embed the data
X=embed(y,d,t);
[dx,nx]=size(X);
%find the nearest neighbours of each point
ind=nearest(X(:,1nx-kth)),tau); %whooh hooo!
%distance between each point and its nearest neighbour
d0=rms(X(:,(1nx-kth)))'-X(:,ind)');
%... and after one time step
d1=rms(X(:,(kth+1):nx)'-X(:,ind+1)');
%exclude any coincident points
d1(d0==0)=[];
d0(d0==0)=[];
%calculate the proportion fnn
ifnn=sum((d1./d0)>th)/length(d0);
%disp
disp(['tau = ', int2str(t),', de = ',int2str(d),', nfnn = ',num2str(ifnn*100),'%']);
px=[px ifnn];
end;
p=[p;px];
end;
p=p';
  • #373
  • Edited 1:34pm Feb 15, 2009 12:51pm | Edited 1:34pm
Quoting anx
In the spirit of collaboration.......
The curve looks really pretty but I assume this indicator repaints the past as I tested it inside an EA and the results were not what I expected by looking at the curve - ea's are pretty good at testing because they calculate the indicator values as they would be calculated in live trading [with some exceptions of course].

I attached an image that I can't understand unless the indicator repaints (example of one such strangeness marked with red arrow up). EA I used is really simple, it closes shorts/opens long when curve turns up (ssi at open is > than ssi at 1) and vice versa on turn down.

I can post the profit curves from my test EA if you are interested. edit: attached 20 year (1990-today) daily profit curve for EURUSD
Attached Image(s) (click to enlarge)
Click to Enlarge Name: whipsaw.gif Size: 17 KB
Click to Enlarge Name: 20ssa.gif Size: 11 KB
  • #374
  • Feb 15, 2009 1:34pm Feb 15, 2009 1:34pm
Quoting mikkom
The curve looks really pretty but I assume this indicator repaints the past as I tested it inside an EA and the results were not what I expected by looking at the curve?

I attached an image that I can't understand unless the indicator repaints (part marked with red arrow up). EA I used is really simple, it closes shorts/opens long when curve turns up (ssi at open is > than ssi at 1) and vice versa on turn down.

I can post the profit curves from my test EA if you are interested. edit: attached 20 year (1990-today) daily profit curve for EURUSD...

Like Codebreaker says , """SSA is non-causal (all the points are calculated from all the other points) so cannot be used directly for trading. But it certainly makes a good noise reducer."""

In this moment you have a good noise reducer, not the holy grail !!!!!
  • #375
  • Edited 2:01pm Feb 15, 2009 1:48pm | Edited 2:01pm
Quoting anx
Like Codebreaker says , """SSA is non-causal (all the points are calculated from all the other points) so cannot be used directly for trading. But it certainly makes a good noise reducer."""

In this moment you have a good noise reducer, not the holy grail !!!!!
I'm not fluent in math lingo [neither am I looking for holy grail here, I already have my own grails]. So what does non-causal here imply? That all of the [history too, not just the last point] calculated curve basically changes at every moment when new data arrives? If that is the case then why are you even talking about this? I just don't get what is the "noise reduction" that you are looking for here - I mean what is the actual hypothesis that you are trying to prove with this?
  • #376
  • Feb 15, 2009 2:54pm Feb 15, 2009 2:54pm
Thanks CB and MisterH for the Matlab code... (Thanks to you too anx, but I may be the only one here without MT4, so I can't use it.) It never ceases to amaze me how much advanced technology is just out there, waiting for people like us to find it and put it to (hopefully good) use. Cheers...
  • #377
  • Feb 15, 2009 3:55pm Feb 15, 2009 3:55pm
I'm with Mikkom on this one: why put 1 second of your time into non-causal methods? It's not a coding error that causes repainting, it's simply useless for trading because it's a conceptual flaw in this context, comparable to the data-snooping bias that has crept in too many "peer reviewed" publications. The SSA does not give you a good noise reduction method, because in real time its values will change, and this will give you only an approximation of noise reduction. Just like the Hodrick-Prescott filter: there is no merrit, no use for trading. Some policy makers base their decisions on extrapolated values of the HP-filter, can you imagine?

Now that we're on the topic: which of these are causal do you think?
- spline smoothers
- kernel smoothers
- local regression methods (like LOESS / Lowess: local polynomial regression)
- wavelets
- running medians
- Savitzky–Golay smoothing filter
- Friedman super smoother
- Wiener-Kolmogorov filter

We've had a similar discussion on ideal timeseries to trade on forex-tsd
  • #378
  • Feb 15, 2009 4:17pm Feb 15, 2009 4:17pm
Quoting Codebreaker
mikkom's point is well made. There is nothing here to say that all the stuff we discuss on this thread definitely works! They are just ideas. It is how you use them that makes the difference.

[..]

[3] The sinusoidal components of such signals have a certain "momentum", and even if they can change quickly, they cannot change instantaneously. Therefore, they will persist a little into the future. Therefore, if we can find the components and extrapolate them we can take a peek a few bars ahead, which is all we need for success. [ABSOLUTELY...
CB,

Thanks for the reply, I didn't notice this before as I said, I removed my subsription and only now went back the pages I missed.

I marked one part of your post bold, that is where I think we don't agree. In fact higher volatility usually means that direction [trend] can and usually will change in an instant and also very, very quick manner so that the momentum will turn exactly to the opposite direction and with the same speed as it went to other.

I attached a picture with places marked X where the price has suddenly turned with no warning. Note the atr below, there are no such spikes there meaning that the volatility can increase/decrease independently of price. And this is daily chart, shorter period charts are even more unpredictable.

Anyway this thread has been interesting to read, when you will find a correct focus [which I don't think the current signal processing stuff is], I think you can come up with some really clever stuff.
Attached Image (click to enlarge)
Click to Enlarge Name: x.gif Size: 18 KB
  • #379
  • Feb 15, 2009 7:29pm Feb 15, 2009 7:29pm
Quoting mikkom
... when you will find a correct focus [which I don't think the current signal processing stuff is], I think you can come up with some really clever stuff.
With all due respect, from the time Codebreaker first started this thread, the whole point has been the application of signal processing to pro-trend trading systems. Let's try to keep the focus and let other threads cover more mainstream topics. Cheers...
  • #380
  • Feb 15, 2009 9:13pm Feb 15, 2009 9:13pm
Let us all not forget the fact that cycles are going to change... and in forex, rather quickly. So, you must find the persistent cycles... those that occur in the current frame of data analysis and in the past. The cycle may not look pretty when overlayed onto current price, but that is how it is. I see that some want the cycles to be pretty and curve fit... that is not going to happen.

mikkom is right when noticing that price can change directions quickly. I would want to take advantage of that fact by noting when price was going opposite of the dominant cycle(s). When it does, you wait until price reverts back into the direction of the dominant cycle(s), and trade it. I believe price must always conform to the dominant cycle.

FFT, SSA, Goertzel are all going to "repaint" due to the cycles changing character. You can't trade it the way previously attempted.

Carl
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