a trading strategy based on Elliott Wave Theory - page 239
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Wiener process
A random process wt is called a Wiener process if it satisfies the following conditions:
1. For any t0 < t1 < ... < tn the increments wt1-wt0, wt2-wt1, ..., wtn-wtn-1 are independent;
2. The random variable wt-ws, s<t, has normal distribution with mathematical expectation 0 and variance t-s;
trajectories wt are continuous.
3. The trajectories of a Wiener process wt may leave any given point wt0, e.g. zero: wt0=0.
In the general case, if a time series can be modeled by the sequence X[i+1]=a*X[i]+sigma, where sigma is a normally distributed random variable with zero expectation, and a is a constant taking values in the range -1...+1, then such series is called Markovian. A special case where a=0 is called a Wiener process. This model, for instance, well describes the random walk of a weighted small particle (Brownian motion).
This is not at all consistent with an average of 5.5 ticks/minute of real data flow.
Yuri, you are confusing the mean and the probable value of a quantity. What you defined as a mean value equal to 5.5 is in fact a probable value and the mean is defined as the ratio of the integral of the distribution function taken over the entire domain of determination to the integral of the same domain from one see Fig.
It is clear that the mean does not coincide with the probable value and is 10. This corresponds to the ratio of the number of ticks to the number of minute bars in time series 1min based on these ticks (data on the number of ticks and minute bars in corresponding series are presented in the chart). The same value (10) is obtained by plotting the volume of one-minute bars for the EURUSD 2006 1min time series and finding the average.
In continuation of our discussion (not to dispute at all), and breaking a little my word: as I wrote earlier, Sergey, you model a Markovian process(Neutron 27.01.07 15:15), but for some reason you call it a Wiener process. How to simulate a Wiener, I think I've already written. And the correct way to model it is with the Monte Carlo method. Exactly for this reason (X[i+1]=a*X[i]+sigma, where a=1), my indicator showed slight dependence between samples, while for a=0 it did not show any dependence.
Good luck. :о)
Instead of "...In general, if a time series can be modelled by the sequence X[i+1]=a*X[i]+sigma,... " should read: "...In general, if the first differences of a time series can be modelled by the sequence X[i+1]=a*X[i]+sigma,... ".
. Actually I meant the mathematical expectation. It is determined simply - by dividing the total number of ticks by the total number of bars. It could be more complicated: we could plot the probability density function and then calculate Xav = Sum(X*p(X)) by all values of X. However the result would be the same.
If in your formula Fusd[j]=j*N[j], where N[j] is the number of minute bars containing j ticks each, it leads to the same results. If Fusd[j] is a function of probability density function, then the integral of it over the whole definition area is equal to 1. And if Fusd[j] is an integral FR, then the integral of it makes no physical sense at all. It seems. :-)
If by probable value you meant fashion, then my number is definitely not it. The maximum of a distribution density function cannot be calculated by simply dividing one simile by another. And that's exactly what I did.
When, Yuri, will you give me the results of your Kagi simulations of real trading?
That's what I'm doing right now. If I can do it in time, I will do it today.
I am wildly sorry, but in the post with the results of the simulation of real Renco H-build trades the file names of the ticks were mixed up, as a result the ticks for the corresponding pairs for 01.11.2006-29.12.2006 took part in the test... i.e. for a total of two months.
Here are the results for the year:
I would like to draw your attention to noticeable drawdowns!
Alexey, if you don't mind sharing your thoughts (not predictions, not assertions): what is happening now with the pound according to Elliot's wave theory or his follower? Is a repeat of the 1.99 level possible? And in general, is an upward rush possible. I remember that predictions are a thankless business, but still, it's opinion, not assertion, that matters to me!!!
I ask for feedback from supporters of Elliot Wave Theory and get back on topic, as this thread has long failed to live up to its name. I respect, truly respect, mathematicians, statists and programmers (probably future millionaires or already:)), but it's still muddying the waters.
Good day, if you're not joking.
I will share my thoughts with pleasure :)))
I think that in the near future, i.e. after the 2.1000 mark, the same thing will happen to the pound, look here:
h ttp://www.clipfish.de/videoplayer.swf?as&videoid=NzAzfDQ%3D&r=1
Yes, that looks very different !
By the way, a question. For our results to look comparable, I need to know 3 things.
1. For the H+ strategy when the next H-level is reached, the position is a) saved, i.e. actually traded by one lot, the position is opened and held up to the first stop loss, then reversed, but also by one lot; b) added, i.e. at each H-level one lot is added, and so on to the first stop loss, where all open in one direction are closed and one lot in the opposite direction is opened, to which new lots are then similarly added. If not a) or b), how and by how much.
2. For the H- strategy, when the H-level is reached, the position is opened in the opposite direction. If the actual price direction changes, all is well, and after passing H-points, the reversal happens again. Here we are not able to add. If the price does not change its direction, we reach the stop loss. At this point, formally, we should perform two actions: this stop loss is triggered and simultaneously we should open again against the movement direction. If we actually perform these two actions, nothing changes in the position, but we lose the spread. I have not seen how Pastukhov handles stops. Explain to me how you did it, and I will repeat it for kaga.
Did you use any formal restrictions (e.g. on the size of deposit, etc.), which somehow affect the number of operations, or put a pure experiment, where the strategy is tested without any external conditions of application?
Are there any other subtleties I need to take into account to make the results comparable?
1. If it is Mathcad, then trade POINTS. No lots and no fills! We start from zero. The condition to close a position is a price movement of H points against the open position. The condition to open a position is to close the previous position, i.e. we do not use stop orders. Opening is performed on the next tick after the closing. There is no slippage. No requotes. There are no limitations. We trade the entire history. The last opened position is closed by force, and its contribution is not considered in the overall balance. EURUSD spread is 1 point, EURCHF is 2 points, EURGBP is 2 points. All of the above is true for the H and H+ strategies.
2. If this is a MT4 tester (it is not clear how to use ticks in this case), we trade a standard 1 lot. No adding! We start with $10000. Condition for closing a position is a price movement of Н points against an open position. Condition for opening a position is to close the previous position, i.e. we will not use stop orders. In this case I do not know what to do with spread. Everything mentioned above is true for H- and H+ strategies.
In this case, I will have to add my Mathcad code for lot trading and lay out new data for comparison.