Building a trading system using digital low-pass filters - page 11

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How can there be no process, bstone? And constancy - in some statistical sense, of course, not in the strict equality of all counts. Here is the definition given by 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.

The only stationarity test I know of is the Dickey-Fuller test. But it assumes some model of the process (in this case 1st order autoregression). But what if the model is not known to us beforehand?


Let's start with the simplest one: "MOJ is constant (independent of time)". How would you practically test this? Calculate the moving average of the process (that's what the OIM is)? With what period?

 
Well, it's all there in the definition: the m.o. must be invariant with respect to the time shift. In fact, this means that if you make a series of measurements of the process under study, given some period (the period does not have to be the same, but it must be large enough for the statistical validity of the resulting estimate of m.o.). Each measurement covers a separate part of the series (shifting the time), the more parts, the higher the reliability.

As a result we get a series of measurements (not a process), from this series of measurements we get an estimate of m.o. with the appropriate statistical characteristics. That's it.
 

bstone, this is all understandable - and at the same time you haven't told me anything new. What should be the averaging period to get a current IOJ estimate? Let's say I have 14,000 counts. Is the period 10, 50, 100 or 200?

And what should be the variance of the OLS to consider that the hypothesis of invariance of the OLS over time is not rejected?

 
Mathemat:

bstone, this is all understandable - and at the same time you haven't told me anything new. What should be the averaging period to get a current IOJ estimate? Let's say I have 14,000 counts. Is the period 10, 50, 100 or 200?

And what should be the variance of the OLS to consider that the hypothesis of invariance of the OLS over time is not rejected?

Well, if I haven't reported anything new, then it's time to remember the concept of the confidence interval. In this case, the size of the period depends only on your claims about the accuracy of the result obtained. That is, you can set a suitable confidence interval for the estimate of m.o.s. for a particular plot, in order to find out the required size. Then you can do the same with calculating the required number of plots for the final estimate.

There are different methods for calculating the confidence interval. You may have to first identify and prove that the measurement results conform to known distributions (for example, the method for calculating confidence intervals by Student's distribution generally only works for samples from normally distributed populations).

It is possible that already at the stage of attempting to identify the law of distribution of measurements you may find that stationarity is not to be expected.

P.S. I am actually a manager, so I have a relatively superficial knowledge of statistics, but this is what common sense dictates, based on what I know.
 

To Mathemat

I tested the return distribution (EURUSD 240) against a normal distribution. (NRD) according to the chi-square test of the Pearson test is not NRD. I am attaching the file with detailed explanations (matcad); it also contains the estimation of ORM and RMS and the calculation of the confidence intervals of the estimates

I think one conclusion from this research is useful, it is the recommendation to set SL at 4H for this currency pair, it is 81 points (3*SCO). Who wants, you can download and check your favorite currency. If something is unclear about the program and calculations, please contact me on Skype, I will try to help.


Z.U. Prove that this series is stationary in the narrow sense failed. I will try to do further research to prove stationarity in the broad sense (MOG and RMS (covariance) = const).



To NorthernWind

The graphs you have shown are not the numerical series that the mathematician is asking to investigate. In 5-10 min. I think I will post studies that confirm the cyclic nature of the candlestick value.

Files:
11.zip  273 kb
 

To NorthernWind

I took EURUSD60 and made analogous constructions but for a series of numbers H - L

Here is ACF. You can visually see that it is not a delta function and there are some stable oscillations in the process + exponential decay

ACF spectrum

In the spectrum there are two distinct oscillations with periods of 12 and 4 hours.

The file is attached.

Files:
22.zip  1292 kb
 
Mathemat:
Prival: ok. ok, i'll try to check tomorrow using Pearson's neumann criterion. But it's still not clear to me how to model without a trend ? Alexei: The modelling methodology is not clear.
I described this method briefly here: https://forum.mql4.com/ru/9358/page6#51829 . It also says what I need it for.

And the trend still appears when integrating a series of returns (it recovers unambiguously).

I think you are still wrong, it is noise and it is stationary. The trend is non-stationary. That is why I think that even if we mathematically strictly model returns we will not be able to restore the trend unambiguously.
 
Mathemat:

bstone, this is all understandable - and at the same time you haven't told me anything new. What should be the averaging period to get a current IOJ estimate? Let's say I have 14,000 counts. Is the period 10, 50, 100 or 200?

And what should be the variance of the OLS to consider that the hypothesis of invariance of the OLS over time is not rejected?


See file 11.zip for how to calculate the confidence interval of the IOJ estimate.
 

I would like to reiterate my point, return is noise. It is what prevents us from seeing the trend (what moves the market) on which we can make money. But I do not know how to filter it. Look, even if it's not NZR, it doesn't move anywhere near zero, and that's all. And take the integral and here it is a trend...

 
Prival:

To NorthernWind

The graphs you presented are not the numerical series that the mathematician is asking for. In about 5-10 minutes I think I will post studies confirming the cyclicality of the candle size.


So, isn't H-L the same thing?
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