From theory to practice - page 443
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So far, +4% for the month. But compared to the results in one of the neighbouring threads, it's nothing.
By the way, the yield by itself does not say anything. It is common for clever people to state it only in conjunction with the drawdown and the period.
Alexei, do you have any data - how does the distribution of increments of any pair change from year to year? Can we say that when sampling ticks per year, the non-parametric statistical moments (median, median deviation, etc.) of the increments are almost the same?
I have this suspicion that, yes - we are dealing with the same probability distribution from year to year, and the non-stationarity only appears at different parts of the sliding time window.
Still, I prefer to refer to it as "you", if you don't mind. I'm more comfortable that way.
There is an implicit assumption in your question that it can be answered unambiguously by examining a sample of increments. This is incorrect for a process with non-stationary increments. In addition to sampling, there must be a parametric model of the process. And sampling only allows us to refine these parameters. That is, with the same sample and different models the answer may be different.
Partitioning the process into stationary chunks is just one such parametric model. The problem is that such a partitioning is far from unique - different people will always mark the trends differently and they will have different answers to your question.
Alexander_K2:
But if I had C=const,
i.e. the speed has to be constant? Then it turns out that you cannot count the speed from the price increments.
D=sqrt(C*lambda*t) diffusion process variance
This is an average value, for theorists. A random process can realise completely different trajectories with the same C, t, and lambda.
So it will be much more accurate to measure the variance already realised (bollinger, etc.) rather than calculate the theoretically implied variance.
Another D for your understanding of random processes)
What I'm asking is this.
Here tonight, my TS just miraculously avoided overnight trends in AUDCAD and AUDCHF. Before 00.00, the speed, tick volume, etc. dropped sharply. Consequently the variance has decreased. And this in a sliding window = 4 hours!
But if I had C=const, i.e. average speed at t --> to infinity, there would be nothing wrong.
Your method of price analysis is obviously inconsistent with your trading system. When trading, you care about every little trend like that, and when calculating the sample distribution (and any sample values) you mix all those trends into one pile and average them out\compensating for each other. Shuffle a sample of increments randomly and you'll see that the price graph becomes quite different, while the sampling characteristics remain the same. Sampling will never give you all the information you need, you need a process model.
So, in your opinion, choosing some sliding windows and calculating averages in them is the wrong way round?
And who knows the right way, I think this window may change depending on the situation.
And who knows the right way, I think this window may change depending on the situation.
Quite agree. Only this dependence will also change over time (non-stationarity). That is, in my opinion, any Grail in reality will be subject to constant wear and tear and sometimes sudden breakdowns)
Built a meter like this. (Click on the picture for animation)
The Market Calm parameter was so named because.... , but just . I came up with a formula, but I don't know what it will do.
Still, I think that if you look at non-parametric statistics, a meaningful sample of increments will always have the same values.
Just as the absolute median deviation for a moving tick sample (of 1,000,0000 elements) = 0.00002, it will forever remain so for a particular pair.
The median deviation does not "notice" well the change of distribution tails, that is why it is more stable to outliers than the standard deviation. There are no measurement errors to be discarded in prices, on the contrary - outliers are very important.
This is what the distribution of the "memory" function looks like for EURUSD in the sliding window = 1 hour over the last 3 weeks:
On the right we see a giant "tail", which says that in those sections where it appears, i.e. "memory" appears, no Ornstein-Uhlenbeck model or "return to the average" is out of the question.
But how to determine the threshold value - I don't know yet. By persentiles, of course. But =0.99 or 0.999 - I don't know. I can't justify it yet.
Here comes the obscurantism in all its glory again)) The rate at which quotes come in depends on server load and internet - even the hedgehog understands that.
It has nothing to do with memory or forex models.