Regression equation - page 2
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Well, get an empirical distribution of errors when approximated by a polynomial. And compare it to the normal one. Pay special attention to the tails, not to the central part.
Are we talking about selecting the best (in the sense of MNC) polynomial parameters?
Or are we talking about choosing the best ones in a different sense?
Or are we talking about the correctness of the polynomial for the approximation?
I asked for an explanation of the inefficiency of MNC to calculate parameters of a pre-selected function (after all, the reason for thick-tailedness may be in an unfortunate function :).
And if there are similarly simple procedures for determining these parameters - I'm happy to get acquainted with them.
But I'm surprised by the formulation of the question: since there are tails in errors, it's no good MNC...
;)
Better to use LAD or quantile regression. This is more complicated (you will have to code much more, and you will have to plug it into science), but it works...
What, the truth for quotes works? Is there objective evidence for this?
P.S. Imho, any approximation pretending to extrapolate assumes stationarity. Fat tails (again imho) just represent stationarity breaks, i.e. the attempt to take them into account will not add anything concrete to the prediction. So it will widen confidence intervals, making the prediction useless, and what good will it do us?
But this is all speculative reasoning, I'd be happy to see some real data to refute it
P.S. Imho, any approximation pretending to extrapolate assumes stationarity. Fat tails (again, imho) just represent stationarity discontinuities, i.e. trying to account for them will not add anything concrete to the prediction. So it will widen confidence intervals, making the prediction useless, and what good will it do us?
But this is all speculative reasoning, I would be glad to see the real data to refute it
Evaluation of regression parameters in multicurrency analysis may not involve "straightforward" extrapolation, and taking these parameters into account, for example in trading on less liquid pairs - allows you to get some statistical advantage (because we do not trade in the market, but based on DT quotes).
But the spread is too big...
But nevertheless - if the majors move significantly, the minors will behave as "written".
;)
FreeLance:
But nevertheless - if there is significant movement in the majors, the minors will behave as 'written'.
What, the truth for quotes works? Is there objective evidence for this?
P.S. Imho, any approximation pretending to extrapolate assumes stationarity. Fat tails (again imho) just represent stationarity breaks, i.e. the attempt to take them into account will not add anything concrete to the prediction. So it will widen the confidence intervals, making the prediction useless, and what good will it do us?
But this is all speculative reasoning, I would love to see real data disproving it.
I will try to explain it theoretically as I am not ready to present my calculations as they are raw.
During my research I tried to present the price time series as a sum of two stationary (!) processes: a) Gaussian with significant correlations up to 2-3 counts (strictly speaking, it is quasi-stationary, because the characteristics are still a bit "floating") and b) Poisson flow of responses to external influences. The first is something we all know what it is. The second is just what you called "stationarity discontinuities" and which does produce thick exponential tails. But if we take this particular model into account, it turns out that the non-stationarity of the quote stream we see on the screen is apparent - in fact the sum of the two stationary processes is stationary in both the broad and the narrow sense.
By approximating with MNC we force the regression polynomial to "cling" not only to the normal part of the process, but also to the Poisson outliers, hence the low prediction efficiency which, generally speaking, we need for . On the other hand, by taking quantile polynomials we get rid of the second, Poisson part of the process completely: quantiles simply do not respond to it, and absolutely. Thus, by identifying the places where the regression gives significant attempts, we can thus almost online localize "failures" with a high degree of certainty (predicting them is probably not yet possible, as there is no appropriate model, at least, I do not have:).
I will roughly (very) give my comparative results (they were done half manually): efficiency of stationarity discontinuity localization (frequency of its correct detection on the first bar) for MNC is about 0.55-0.6, for quantiles - 0.85 and more (there's plenty of work to be done). This is the gain.
By approximating with ANM we force the regression polynomial to "cling" not only to the normal part of the process, but also to the Poisson outliers, hence the low prediction efficiency, which, generally speaking, we need for . On the other hand, by taking quantile polynomials we get rid of the second, Poisson part of the process completely: quantiles simply do not respond to it, and absolutely. Thus, by identifying the places where the regression gives significant attempts, we can thus almost online localize "failures" with a high degree of certainty (we probably can't predict them yet, as there is no appropriate model, at least for me:)
Hmmm. so it's exactly the opposite, not a widening of the confidence interval, but a narrowing. Very interesting, have to read it, thanks.
About being stationary and the discontinuity process of course one wants to argue. But there are no arguments, so there is only one thing left to think about.
Maybe you've solved the problem of time, too? :) I mean the problem of choosing the window size.
In my research I have tried to represent the price time series as a sum of two stationary (!) processes: a) a Gaussian with significant correlations up to 2-3 counts (strictly speaking, it is quasi-stationary, as the characteristics do "float" a bit) and b) a Poisson flow of responses to external influences. The first is something we all know what it is. The second is just what you called "stationarity discontinuities" and what really leads to the formation of thick exponential tails.
Interesting, interesting. Candid, do you remember my thread on Inhabited Island about a metamodel with a quasi-stationary process (diphurs there, also the rabbit out of the hat we pulled)? Something very similar. The noosphere does exist, after all, and the thoughts in it are common...
Maybe you've solved the time problem too? :) I'm referring to the problem of selecting a window size.