Building a trading system using digital low-pass filters - page 15
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bstone
I think the problem is that it is theoretically impossible to make money on your generated series
That's what I'm saying about the price series, there's a definition of BGS through a Wiener process, and vice versa. And it has already been proven that "if" the market model is an integral of the Wiener process, then you can't make money in the long run, especially if you play with a spread.
OK, bstone, now you've misunderstood me. What is the real distribution, I know approximately from Peters work (fractal Brownian), and I can generate value with such distribution, it is not difficult. But this is only a general picture, integral, so to speak. And Peters gives no guarantee that the same picture will be repeated for any piece of the series (and it is a necessary condition for the series to be stationary). So it is not a solution.
What I need is to find such a reversible transformation of the original series of quotes that it gives a stationary process with some certainty.
I hope those who have been "in the loop" for a long time will also look at these explanations... And once again, I don't intend to profit from my synthetics. I only need them for testing purposes.
I'm talking about the price series, there is a definition of GSC through a Wiener process, and vice versa. And it has already been proven that "if" the market model is an integral of the Wiener process, then you cannot make money in the long run, especially if you play with a spread.
Ah for that matter. Yeah, no argument there. There is such a proof. But one can also approach it from the other side.
Let us imagine that there is a non-zero probability that I can guess local lows and highs on a generated chart for a long enough time. This probability may be as small as I like, but nevertheless, probability theory unambiguously tells us that it does not mean that an event with this probability will not happen today or tomorrow. In general, if I am lucky enough to guess lows and highs on this chart from today (within the required long term perspective), I will earn in the long term.
We get a contradiction. Of course, it would not be a significant contradiction if the long-term outlook was an infinite time horizon.
bstone
I cited this as opposed to your proof that the visually generated series is very similar and the elioters will find anything here. It's more a question of adequacy. There are many ways to generate a price series but how can we rigorously prove that it is adequate to the true price series? Can you help with that? Do you know any methodologies for this?
OK, bstone, now you've misunderstood me. What is the real distribution, I know approximately from Peters work (fractal Brownian), and I can generate value with such distribution, it is not difficult. But this is only a general picture, integral, so to speak. And Peters gives no guarantee that the same picture will be repeated for any piece of the series (and it is a necessary condition for the series to be stationary). So it is not a solution.
Exactly, you know the approximate distribution obtained by Peters. And you can build a histogram of the real distribution in the study area. Generate as many samples as you need that fit with due precision into this real distribution. And use them for testing of alternative behaviour of the TS under study on characteristics of the initial plot. This is an effective way of modeling, more effective than using an approximating theoretical distribution.
Well you can of course ignore this approach and look for a way to go from non-stationary series to stationary series. Only I understand that this is a pipe dream within a tangible future :) Just remember sometimes that aeroplanes and other technical devices owe their existence largely to an engineering approach rather than purist mathematics.
Ah for that matter. Yeah, no argument there. There is such evidence. But one can also approach it from the other side.
Let us imagine that there is a non-zero probability that I can guess local lows and highs on a generated chart for a long enough time. This probability may be as small as I like, but nevertheless, probability theory unambiguously tells us that it does not mean that an event with such probability will not happen today or tomorrow. In general, if I am lucky enough to guess lows and highs on this chart from today (within the required long term perspective), I will earn in the long term.
We get a contradiction. Of course it won't be as significant if the long term is understood as an infinite time horizon.
bstone
I cited this as opposed to your proof that the visually generated series is very similar and the elioters will find anything here. It's more a question of adequacy. There are many ways to generate a price series but how can we rigorously prove that it is adequate to the true price series? Can you help with that? Do you know any methodologies for this?
bstone, this is just sophistry, not a serious argument. There is a proven theorem that you won't make money on a Wiener process long term. Full stop.
Please bring me one rigorous proof that you can make money in the long run on a real price series process. Until you can do so, the argument against my proposed approach is highly questionable. Do you agree?
bstone
In principle there are many ways to generate a price series, how can you rigorously prove mathematically that it is adequate to the true price series?
What are the criteria for adequacy?