Building a trading system using digital low-pass filters - page 7

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Prival:

A random process (SP) with finite variance is called stationary in the broad sense if, its OLS (m.o.) and covariance function are invariant with respect to time shift, i.e. the OLS is constant (not time dependent) and the covariance function depends only on the difference of arguments t 2- t 1.





In some cases (which seems to me to be our forex case) a non-stationary process can be transformed into a stationary one.







Obviously it reduces to stationary. Most probably we are dealing with so-called periodically stationary or cyclostationary process.





Mathemat I gave you Tikhonov, it seems to have it all

I don't think I have such a textbook. Thank you.
 
I have pieces of the book scanned, but they don't fit on the forum anyway. If you don't mind, I can transfer them via Sype, which would be more convenient and faster.
 
bstone: I don't understand what the problem is exactly? There is a clear mathematical notion of a stationary random process - it is a random process whose probability characteristics do not change over time.
Ok, Roman, if everything is so obvious to you (ok, "for you"?) tell me if the process is stationary [i] = Close[i]-Close[i+1] (in MQL4 notation) in a broad sense, for example on H4 from 1999 to EuR? I still don't know it. And I still don't know what characteristics of this series I need to know to be sure.
 
Mathemat:

Ok, Roman, if everything is so obvious to you (is it ok for you?), tell me if returns[i] = Close[i]-Close[i+1] (in MQL4 notation) is stationary in a wide sense, for example on H4 from 1999 to eu? I still don't know it. And I still don't know what characteristics of this series I need to know to be sure.

Well I gave a definition from memory. But better pay attention to Prival's answer. There is an algorithm for determining stationarity in the broad sense of the series you are interested in: finiteness of dispersion and invariance of m.o. and cov. fii nance with respect to the time shift. Count dispersion, shift time, count r.o. and cov. fie. Then draw conclusions. My money's on non-stationarity. :)
 

I will try to answer for Roman. This conversion reduces BP prices to stationary, to BGS

here's the original BP

Here is return

Here is ACF (autocorrelation function return), it looks like a delta function, i.e. similar to BGS, let's check it by plotting the spectrum

spectrum

The spectrum is uniform throughout the frequency domain, i.e. it is a CMP. Thus the transformation reduces the BP to a stationary process.

Z.U. This is the basis of the proof that one cannot make a profit (Wiener process). But this transformation kills the trend, which is exactly what one can earn on. IHMO.

 
bstone: I'm betting on unsteadiness. :)
Yeah, right, I agree. I'm not sure, but I agree. And what is permanence in the strict sense? Prival, explain, eh? I did not see it in Tikhonov's work. Shit, how can a process be stationary or not, damn it!

Prival, you reduced it to BGS. OK. You tell me - is it stationary or not? I personally don't care if it makes money. I care if it's stationary or not - and in what sense. I'm a pure scientist, Privalych. Do you understand me? I mean, how do you know you've got a BSH?
 
Z.U. This is what the evidence is based on, that you can't make money (Wiener process). But this transformation kills the trend, which is exactly what you can make money on. IHMO.

Why does it kill the trend? It seems this question has already been discussed in another thread. The trend remains a trend after reverse transformation from returns.
 
Mathemat:
I'm betting on non-stationarity. :)
Yeah, right, I agree. I'm not sure, but I agree. And what is consistency in the strict sense? Prival, explain, huh? I did not see it in Tikhonov's work. Shit, how can a process be stationary or not, damn it!

Prival, you reduced it to BGS. OK. You tell me - is it stationary or not?


Stationary in both the narrow and broad sense. Can=constant, sko=constant.

Sign of GBS -> ACF = delta function

 
bstone:
Z.U. This is what the proofs are based on, that you can't make money (Wiener process). But this conversion kills the trend, which is exactly what you can make money on. IHMO.

Why does it kill the trend? It seems this question has already been discussed in another thread. The trend remains a trend after a reverse conversion from returns.

Yes, the inverse reconstructs with accuracy to the initial constant, but there is no trend in returns, there is only noise. That is why if we apply it, it is a deadlock, there is nothing to analyze. We should reduce it to stationary by another way, as I said earlier in this thread.
 
Prival: stationary in both the narrow and broad sense. can=constant, sko=constant.
Wow. Privalych, you've made me so happy. I'll sleep well now. Thank you, my dear. Of course you overdid it, but the narrow one is enough for me. Let the MO, RMS and AF be constants (statistical), and the rest - to hell with it ...

P.S. And how did you determine that what came out is BGS (strictly)?
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