Stochastic resonance - page 30
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
...I have an interesting question along the way. Can someone enlighten me as to why such a simple and convenient distribution function with good properties is not used in statistics? And if it is used, why isn't it written about? I've never seen anyone try to approximate an incremental distribution other than the lognormal.
Yura, I don't know the answer to this question.
I can only assume that your proposed distribution p(X)=A*(X^a)*exp(-B*(X^b)), is a particular case (e.g. Generalized Exponential Distribution p(X)=a/(2G[1/a]*l*s)exp{-[(x-m)/l*sl*s]^a}, Bulashev, p.41), or those few, who also managed to get to the bottom of it, decided to keep silent and quietly mow the cabbage on the vast Forpolye:)
I thought so too, and it would be, if the generalized distribution had an exponent. Since there is no such thing, the generalized distribution is nonzero at zero and extends to the region x<0. The exponent makes the left slope very steep (in the generalized one with a<1 both slopes are gentle), and the right slope is even flatter than in the generalized one. I won't hesitate to use that word - thick tail. :-) And, most importantly, it does not integrate explicitly.
But I have a counter-question!
Some time ago I was studying autoregressive models of arbitrary order (when we look for the dependence of the amplitude of the current bar and its sign on the sum of actions on it of an arbitrary number of previous bars). I solved this problem so well that I could not tell if the model series was real or not by its appearance, but for one exception - the distribution function (DP) of the model series was far from reality. I could not find the reason for the discrepancy. Intuitively I felt that the coincidence of the autocorrelation functions was sufficient to match the PDF of their first differences. Turns out it wasn't... There's something I'm not taking into account in modelling the behaviour of the residuals series.
What do you think about this issue?
Since I know neither the methods you used to solve this problem, nor the method for modeling residuals, and my left hand and both feet are lame in mathematical statistics, I, alas, cannot say anything. To at least start thinking about it, this little paragraph alone is not enough for me personally, I need more information to think about it, like Stirlitz.
It is not about calculating Ymin and Ymax per se. It's about recalculating from the original set of derivative set data. Also, your method of recalculating normalisation is arbitrary, tied to the historical set on which you are doing it. When you switch t/f it can change from 2000 bars to, say, 500000 bars. Reaching the range boundary in the first case says nothing, but in the second case it says a lot. You can accuse my method of arbitrariness only with a model distribution function in mind. However, if the real, experimentally constructed distribution based on the "maximum available" amount of data is well approximated by the model distribution, then what's the arbitrariness?
I had no complaints about arbitrariness, for phenomenology the only constraint is accuracy of approximation, and I would prefer to call arbitrariness not arbitrariness, but degree of freedom :)
I'm going to step in here, Neutron. I am not a statistician, so I had to ask the question on mexmat.ru. It is here: http://lib.mexmat.ru/forum/viewtopic.php?t=9102
Question: what information about the stationary process is enough to reproduce it correctly? The answer was: one must know the covariance function and the m.o. of the process. I do not yet know how to build a process with a given covariance function. But the idea is that the resulting process could be considered a proper implementation of the original simulated process. Maybe your process was not stationary?
P.S. I want a plausible simulation of the residuals process (returns). According to Peters, the distribution of the residuals is fractal with acceptable accuracy, and the process is stationary. Although other models are not excluded...
Hi Mathemat!
I'm a statistical dilettante (let's leave the contrary statement to the conscience of Jura) and I simply do not know the answer to most questions:(
A series is called strictly stationary (or stationary in the narrow sense) if its FR, mean and variance do not depend on time.
A series is called weakly stationary (or stationary in the broad sense) if its mean and variance do not depend on time.
Indeed, our series of first differences is not stationary even in the broad sense of the word - the amplitude varies noticeably, do you think this might be the cause of the observed effect?
P.S. I wonder what Peters meant by the stationarity of this process?
I don't like to argue about theoretical questions, I very seldom manage to make up my mind :). In this case, there was no attempt to make a universal assessment. I simply tried to understand and compare the actual volume of calculations "for myself". It seems to me for your approach here it is necessary to include calculation of characteristics of an initial series that in my approach it is not required. The second point - it is not clear what you will calculate for Y, more complex than a simple average. Doesn't the necessity of processing of initial series make your method as sensitive to timeframe as mine? I understand, it is the specifics of the original series. But I have a similar trump card - the found invariant, the same for all tested symbols (majors) and for all timeframes.
I had no complaints about arbitrariness, for phenomenology the only constraint is accuracy of approximation, and I would prefer to call arbitrariness not arbitrariness, but degree of freedom :)
I'm not arguing. I'm just making an excuse. :-)
Calculations for non-trivial averaging methods are a dark forest. I don't go there, I'm afraid. I've solved my problem, and that's fine.
P.S. I wonder what Peters meant by the stationarity of the process.
Maybe that the slope of this process has no convergence limit? :-)))
By the way, Neutron, could you explain one detail to me. What is bad about MO<SCO, and what is good about the other way round? This question came up once, and the FR I used just has this bad property.
Mathemat, maybe you know it too, so explain it to an illiterate person.
Vinin' s question came up here: 'Beta distribution'. This is a specific task, all depends on the branch author's goals. In general, there is nothing wrong with MO<SCO. The situation is the same: on the daily markets MO is a few points, even on the trend from 2001 to the Euro, and RMS is at least dozens of points. On the same Hebrew trend the MoD is about 0.2 points, and the RMS is a few points minimum.
If it is in the same trend, it is not good. The main trade characteristic is the profit/risk. The risk is determined by the volatility, the systematic IRR. There are even such indicators - Sharpe (Profit for the period/SCO), Sortino - the same but taking into account "volatility down". If the RMS is greater than MO, then the loss from that volatility is likely to exceed the potential return associated with positive MO.