Ward 6 - page 17

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alsu:
Moreover, with certain signal characteristics, it is quite possible to build a counterexample - a non-lagging, and even a leading linear filter.

You can't. A leading-edge filter is, by definition, looking into the future. I was only talking about non-linearity and non-lagging. Without looking into the future, but still not necessarily linear or nearly linear with slowly changing parameters, but any physically realizable (not looking into the future again I say) algorithms.
 

So there you go. I wanted to show one of the old ideas. Where it is not immediately obvious that everything is based on SMA. Which is inevitable if you average data from the past in any way, even in a very twisted way.

So: let us introduce two curves. EURUSD and GBPUSD. I will further call them conditionally ED and PD. Can someone draw some additional curves, EDq (it will be drawn in the ED chart) and PDq (we will draw it in the PD chart), such that the difference of EDq and PDq should be leading the difference of ED and PD by some predetermined number of bars (let it be a bar), and the sums coincide: EDq+PDq = ED+PD. Can anyone? :-)

 

I can. But I opened the old file and saw that it was in EURJPY and USDJPY. Not going to redo it. I would have to reverse GBPUSD. That's not the point. So, there isEURJPY and USDJPY. Let's call them EY and DY. We have to plot the additional curves EYq and DYq, so that their sum is equal to the original curve, while the difference is ahead by a bar. Let's assume that a = 288 bars (M5, total of 1 day). See picture. It shows 2 days (2*288 bars M5).

the drawing is elementary. anyone can do it. the question is, how can it be used? :-)

 

Hint:

 
Dr.Drain:

For linear ones, there are. Strictly. Long before your time. There's even such a theorem. What's a "filtering signal"? 0_о

filtered, my mistake.

And there is no proof, don't talk nonsense. There simply can't be one, as, again, there are an infinite number of counterexamples.

 
alsu:

filtered, mistakenly.

And there is no proof, don't bullshit. There simply can't be one, as, I repeat, there are an infinite number of counterexamples.


I'm sending you to the library to read linear filter theory. Yes, by the way, you can practice making up counterexamples. Namely one. Namely one linear filter, in which the lag and the degree of smoothing would not be connected unambiguously and known how.
 
Dr.Drain:

I send you to library, read the theory of linear filters. Oh, by the way, you can practice making up counterexamples. Namely one. Namely one linear filter in which the lag and the degree of smoothing would not be connected unambiguously and known how.

I am sending you to the library to read the theory of linear filters. I've already done that.

A counterexample to your teeth to study - any MA(N) process with one or more first coefficients equal to zero admits the existence of an inverse filter that uniquely reconstructs future values from past ones.

 
I will also add AR processes, even simpler.
 
I am not interested in your processes. Of course, if I take a sine wave as a 'process', I can predict it into the future and filter it out with a prediction. I asked for an example of a linear filter algorithm, not an example of a filtered signal.
 
Now, you will notice that the right area in a bars, where we simply "drew" the q-curves as a straight line for the difference (naive forecast, we are entitled) is somehow related to future for the price itself .We have put our own hands in ahead by a bar. And in terms of looky-loos ... not direct ... :-) I'll tell you right away there's nothing of value here, as it turned out later. But I think many people's hands will shake now when they try to think about it :-)
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