Econometrics: one step ahead forecast - page 122
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Less emotion.
There are no "trends" of which you speak.
What do you mean there are none? Justify, what is there?
There are no "trends" of which you speak.
What do you mean there are none? Justify, what is there?
Suppose price is generated by a process of the form dS(t)=mu(t)*dt+sigma(t)*dW (or dS(t)=mu(t)*S(t)*dt+sigma(t)*S(t)*dW, then we are not talking about price increments, but about logarithms of relationships), where mu(t) is the drift ratio, sigma(t) is the volatility ratio.
If you are talking about trends - mu(t) should be different from zero. Try to construct mu/sigma estimates, prove their unbiased/sustainable/effective (by the way, don't forget to attach something like COGARCH(p,q) to the sigma(t) model).
If the trends are real and you manage to estimate the parameters accurately - you will be able to forecast prices using this model, and there will be a positive correlation between price increment forecasts and actual price increments (not that this is enough for trading).
p.s. You can make a simplifying assumption that mu(t) is a piecewise constant function. Then we can try to use least squares method and Chebyshev inequality.
What do you mean, no? Justify, what is there?
Emotions are long gone, and that's bad :(
I was giving a very simple example of "trends" on a random series that are nothing more than an illusion. You see, a quote is a very complex multifractal that is not even self-similar at all, it is so complex that the order in a quote manifests itself in the highest degree of manifestation of that order - in chaos. Everything is different there.
Geez, well it makes no sense to assess correlation on a primary series. Correlation is a statistic, e.g. you take 1000 cases and want to estimate correlation per lag. For the eurik one point is 0.000001. How far do you think the price will go with such minimal step and with some trajectory deviation properties for such multifractals on the scale of the quote? Of course not, you have this coefficient and it shows a high statistical proximity. See the formula, you had a quotient of 1.5, the price moved away by say 0.0003 (like on the average). Do you think that 1.5 and 1.4997 are statistically close values when you put them into the formula? And so for every range. And the trends in them sit up to oooh :)
Very interesting research was done by Alexei (Mathemat), and I was there :) They were related to evaluating the correlation. But the people didn't show up in any way :(
Suppose that price is generated by a process of the form dS(t)=mu(t)*dt+sigma(t)*dW (or dS(t)=mu(t)*S(t)*dt+sigma(t)*S(t)*dW, then we are not talking about price increments, but logarithms of relationships), where mu(t) is the drift ratio, sigma(t) is the volatility ratio.
If you are talking about trends - mu(t) should be different from zero. Try to construct mu/sigma estimates, prove their unbiased/sustainable/effective (by the way, don't forget to attach something like COGARCH(p,q) to the sigma(t) model).
If the trends are real and you manage to estimate the parameters accurately - you will be able to forecast prices using this model, and there will be a positive correlation between price increment forecasts and actual price increments (not necessarily enough for trading).
p.s. You can make a simplifying assumption that mu(t) is a piecewise constant function. Then we can try to use least squares method and Chebyshev inequality.
Emotions are long gone, and that's too bad :(
I was giving a very simple example of "trends" on a random series, which are nothing more than an illusion. You see, a quote is a very complex multifractal, which is not even self-similar at all, it is so complex that order in a quote manifests itself in the highest degree of manifestation of that order - in chaos. Everything is different there.
Geez, well, it makes no sense to assess correlation on a primary series. Correlation is a statistic, e.g. you take 1000 cases and want to estimate correlation per lag. For the eurik one point is 0.000001. How far do you think the price will go with such minimal step and with some trajectory deviation properties for such multifractals on the scale of the quote? Of course not, you have this coefficient and it shows a high statistical proximity. See the formula, you had a quotient of 1.5, the price moved away by say 0.0003 (like on the average). Do you think that 1.5 and 1.4997 are statistically close values when you put them into the formula? And so for every range. And the trends in them sit up to oooh :)
Very interesting research was done by Alexei (Mathemat), and I was there :) They were related to evaluating the correlation. But the people didn't show up in any way :(
I gave a very simple example of "trends" on a random series that are nothing more than an illusion.
A stochastic trend that is generally indistinguishable from a deterministic trend - saw an article with evidence.
You see, a quote is a very complex multifractal that is not even self-similar at all, it is so complex that order in a quote manifests itself in the highest degree of manifestation of that order - in chaos. Everything is different there.
Let's leave difficulties aside, including fractals.
We are talking about something else entirely. There is a problem of non-stationarity. We are trying to solve at least something, you know, at least something.
Man, it doesn't make sense to estimate correlation on a primary series. Correlation is a statistic, for example.
For me, there's no problem with correlation - it's a fuzzy thing altogether.
I take the quotient and calculate the ACF. I see autocorrelation. To me it is an indication of the presence of a deterministic component. On the one hand it is good as its presence is a chance for success. On the other hand it is bad because while there is a deterministic component nothing can be said about statistics in general and about correlation in particular.
I have extracted the deterministic component, what is successful. Looking at the residual - what can be done etc.
From the outset I did not propose to discuss regression, much less the particular kind of regression I set out. The regression given is an element of demonstrating the decomposition of a series into such components as we know how to handle. I showed that it is possible to distinguish two deterministic components and GARCH.
And then there is the question of predictability.
If you're willing to discuss beyond the fractal level, and specifically, go for it. I know for a fact that there is no periodicity in the model, maybe lacking mathematics
Suggest. It's a long way to a commercial product. But in the course of the discussion we will raise our level and the level of the forum without a doubt. And at the same time we will squeeze inventors of bicycles.
Suppose that price is generated by a process of the form dS(t)=mu(t)*dt+sigma(t)*dW (or dS(t)=mu(t)*S(t)*dt+sigma(t)*S(t)*dW, then we are not talking about price increments, but logarithms of relationships), where mu(t) is the drift ratio, sigma(t) is the volatility ratio.
If you are talking about trends - mu(t) should be different from zero. Try to construct mu/sigma estimates, prove their unbiased/sustainable/effective (by the way, don't forget to attach something like COGARCH(p,q) to the sigma(t) model).
If the trends are real and you manage to estimate the parameters accurately - you will be able to forecast prices using this model, and there will be a positive correlation between price increment forecasts and actual price increments (not that there will be enough for trading).
p.s. You can make a simplifying assumption that mu(t) is a piecewise constant function. Then we can try to use least squares method and Chebyshev inequality.
I gave a very simple example of "trends" on a random series which are nothing more than an illusion.
A stochastic trend that is generally indistinguishable from a deterministic trend - saw an article with evidence.
It's hard to believe.
Try to estimate model parameters y(t)=alpha+rho*y(t-1)+beta*t. In case of stochastic trend, it will be rho=1, beta=0; in case of deterministic, abs(rho)<1.
UPD: "beta*t" may be something else, depends on the chosen deterministic trend model.
It is hard to believe.
Try to estimate model parameters y(t)=alpha+rho*y(t-1)+beta*t. In case of stochastic trend would be rho=1, beta=0; in case of deterministic trend, abs(rho)<1.
UPD: "beta*t" may be something else, depends on the chosen deterministic trend model.
To faa
It's not that far away from a commercial product. I mean my system. I confess, I'm not very interested in yours. But I will follow your progress :)
Yeah, like it's not a forum, it's your and faa's private correspondence. Well... Okay, I won't interfere with intellectual conversations of the highest order.
And then and now I, as you like to put it, am not dumb, and I'm responding personally to you. Speak more clearly, or I don't understand this post.
A little humor never hurt. Usually helps.