Regression equation - page 14
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It's a strange question, of course in the percentage of profit per dollar invested. Is there any other measure in the market?
If a Chinaman is given a fork instead of sticks, he won't notice any advantage of the fork either...
I told you that quantiles and MNCs are completely different things. You take the trading method for MNCs and replace the MNC regression in it with a quantile regression. And the point?
So you can cram any regression into your TS and talk about lack of advantage. You don't have to bluntly substitute other formulas, but change the method itself, proceeding from the nature of constructing the main tool - regression.
I told you that quantiles and MNCs are completely different things. You take the trading method for MNCs and replace the MNC regression in it with a quantile regression. And the point?
I guess I know how and what I use in my strategies. The OLS and quantile are different things, but regression is regression anyway.
It's also dumb aggression, which is what you're showing now.
There's also dumb aggression, you're showing it now.
I agree.
I agree with you there. I'll exercise my right to be a nerd and write something, and you can correct me if I'm rambling.
The idea behind using a regression is that a regression a few samples ahead (backwards) of a sample of its construction will show results close to BP. A regression constructed using ANC on normal distributions is the best solution - it shows the closest results. This is not the case for price BPs. Moreover, for a regression on a price VR to show close results outside the sample of its construction, it does not necessarily have to show close values on the sample of its construction itself. This is a very important observation. I.e. it is possible to construct such a regression that it will show bad results in the sample of its construction and great results outside the sample.
But this is more of a theory. It is very important to understand the meaning of the word "close". Out-of-sample closeness can be assessed using different methods. You can use RMS, you can use median, you can use absolute mean error, etc. There are many methods.
So how do you investigate the regression? Is it good or not? Correct, as I wrote above, goodness of regression is measured by closeness of its values (to BP) out of sample (for a certain number of samples) of its construction.
Let us first decide on a method for determining the closeness. Let it first be the RMS.
We have WR EURUSD of 100,000 samples. We are building the regression on 100 samples. And we will count the closeness for 10 samples forward (backward) behind the sample of its building.
So, we have built the regression on EURUSD using BP data from 1 to 100. We have compared its reading with BP on data from the 101st to the 110th - calculated RMS (let it be RMS1).
Now we have built a regression on EURUSD using BP data from the 2nd through the 101st. We have compared its readings to BP on data from 102nd to 111th - calculated RMS (let it be RMS2).
And so on to the end of EURUSD BP - 100,000 readings.
Got a lot of RMS results: RMS1, RMS2, .... - this is BP. We should investigate it. Look at the mathematical expectation (median) and variance (median variance). Construct the distribution. This result tells us how good our regression is. Let me remind you that we measured closeness through RMS, we could have done it differently.
Now let's take another regression, and obtain also, as written above, its BP RMS.
And when you compare different regressions with their RR RMS, then we can talk about advantages or disadvantages of one regression comparing to the other.
P.S. EURUSD was taken as an example. Of course, one could take BPs of any nature, not necessarily of price nature. For example, BP of Equity TS or something else.
I agree here too. I will exercise my right to be a nerd and write something, and you can correct me if I am rambling.
You're thinking narrowly. All you are saying is autoregression of one BP, but that is only a very narrow special case of using regression analysis. Accordingly, it all depends on what you regress on and what the distribution of the resulting parameter(s) is. If the distribution is normal, then ANC is great. And if it's not normal... And if it is not symmetric... And if one is suddenly interested in the bounds of those parameters... That's where the options come in. The question was about the ISC to the landfill. No, not scrapped, because there are still real trading problems where it works better than others at much lower computational cost.
You are thinking narrowly. All you are saying is autoregression of a single BP, but this is only a very narrow special case of using regression analysis. So it depends on what you are regressing on and what the distribution of the resulting parameter(s) is. If the distribution is normal, then ANC is great. And if it's not normal... And if it is not symmetric... And if one is suddenly interested in the bounds of these parameters... That's where the options come in. The question was about the ISC to the landfill. No, don't throw it away, because there are still real trading problems where it works better than others with much less computational cost.
You see how much you've written, mentioning various nuances in passing. Couldn't I have uncovered them all here. You are given an example, and you make conclusions about narrowness.
I only brought up auto-regression because alsu provided pictures of its use.
My post was not about the peculiarities of regression analysis, but about estimating various regression models. You have to compare regression estimates. And you cannot say unambiguously that something is bad and something is not. The result of applying the regression shows, in particular, the BP of the RMS, as I wrote above.
It is possible to apply regression to any BP, as I wrote above. To autocorrelation residuals, to tails, etc. In general to any. But the methods of regression estimation do not change from the nature of the initial BP.
But the methods for estimating the regression do not change from the nature of the original BP.
The method of regression estimation - yes, but the method itself it can only be of interest to deep aesthetes from pure math. Personally, as a practitioner, I am interested in combined estimation, which includes estimation of regression and at the same time the adequacy of its application. So this combined estimate is measured in dollars. And in my case it showed the advantage of MNC regression over quintile regression, even under thick-tailed distributions. For someone, a quintile regression may be more adequate, if they can convert it into money.
- Do you like cats?
- No.
- You just don't know how to cook them.
So it's not about the adequacy of the regression estimation methods. It was about the adequacy of applying the regression model itself to the original BPs.
The applicability of quantile regression and MNA regression directly to price BPs can be evaluated by the methods, one of which I cited. Obviously, the better the proximity the regression gives, the more you end up with in monetary terms, because better proximity indicates a more accurate (adequate) estimate of future readings.
You compared the regressions in a rather subjective way, simply by fitting them into your TS. I, on the other hand, suggested an objective way of comparing the adequacy of their applicability to the original BPs.
And if it's not normal... And if it's also not symmetrical...
I am interested in your opinion. If we managed to transform the price VR to such a point where its distribution is symmetrical and very similar to normal (I cannot say for sure, as the sample is always finite), what can we do with it? I.e. we can say that the cointegration problem is solved. How do you see further actions in this case?
There is not enough information available. Random walk has a normal distribution. But there is no money to be made from it.
What do you mean by "co-integration problem solved"? The purpose of using cointegration is to get a stationary BP. If it succeeds, you can start cutting cabbage. And it doesn't matter whether this BP is normal or not.