Machine learning in trading: theory, models, practice and algo-trading - page 1792
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oops. Interesting thought. Select/separate sections of a series by the degree to which the model describes the section. Only how to determine at a glance bad or good description of the model of this series. You can't get correlation at a glance. But there is something in it. The question / task is not in the prediction, but in changing the behavior of the series.
Terms and their unambiguity make life easier)))) I have SB initially in the range from minus to plus infinity in infinite time and only then the rules. Wiener's was immediately in the rules)))) apparently that's why it's closer.))
Basically, the usual matstat is a test of statistical hypotheses. For example, let us have only one of two possible models - SB or Ornstein-Uhlenbeck, then we get the problem of distinguishing the two hypotheses, which is solved by the well-known Dickey-Fuller test.
In fact, the usual matstat is a statistical hypothesis test. For example, let us have only one of two possible models - SB or Ornstein-Uhlenbeck, then we get the problem of distinguishing between two hypotheses, which is solved by the well-known Dickey-Fuller test.
The question of the minimum sufficient area for a reliable test))) I don't see how, though, right off the bat. DF test for stationarity, how to apply it to the correctness of the model description?
DF test for stationarity, how do we apply it to the correctness of the model description?
Strictly speaking, it is incorrect - it is a test for the presence of a unit root (this is the null hypothesis) against the assumption that there is no such root (this is the alternative hypothesis). It is NOT true that ANY non-stationarity is identical to the presence of a unit root - the example of an Ornstein-Uhlenbeck process with changing parameters (decoupling) is obviously non-stationary, but is not an autoregressive process with a unit root.
Its applicability to our problem follows from our assumption that any section is either SB or Ornstein-Uhlenbeck, or a switching section between them. Obviously, the small p-value of the test suggests that Ornstein-Uhlenbeck fits more than SB and vice versa. Another thing is that our assumption that only two variants are possible may not be practically applicable and we will have to expand the list of models.
It's a question of a minimum sufficient plot for a valid test.))
This is a complicated non-trivial issue, so it's better to solve it by eye or by selection.)
Aleksey Nikolayev:
1) to use a model to predict prices.
How can a stochastic model make a prediction? It will draw a different trajectory every time it is run. Even if it's similar.
In the standard way - expectation and probabilities of deviation from it by a given value. Another thing is that for SB, for example, this prediction does not make much sense. But for a stationary process (or piecewise stationary) it makes sense. For example, for the Ornstein-Uhlenbeck process (which I actually wrote about) the prediction is to return to the mean.
Strictly speaking, this is incorrect - it is a test for the presence of a unit root (this is the null hypothesis) against the assumption that there is no such root (this is the alternative hypothesis). It is NOT true that ANY non-stationarity is identical to the presence of a unit root - the example of an Ornstein-Uhlenbeck process with changing parameters (decoupling) is obviously non-stationary, but is not an autoregressive process with a unit root.
Its applicability to our problem follows from our assumption that any section is either a SB, an Ornstein-Uhlenbeck, or a switching section between them. Obviously, the small p-value of the test suggests that Ornstein-Uhlenbeck fits more than SB and vice versa. Another thing is that our assumption that only two options are possible may not be practically applicable and we will have to expand the list of models.
This is a complicated non-trivial question, so it is better to solve it by eye or by selection.)
A unit root is the condition of finding the roots of a polynomial equal to (or less than) a modulus of unity. That the series is not wider than a certain corridor. At the edges the roots of the polynomial are 1 or -1. If the roots are greater, the series becomes wider; if they are less, the series is in the corridor. How can this be applied to how well the system describes the series. We should be able to find a system with as few variables as possible that describes the series correctly.
The assumption that there are two states is of course wrong. The same as measuring one parameter, some degree of stationarity will not solve the problem of finding out when the Expert Advisor starts to fail. There is a problem with a large scale series. On each scale, the series behaves differently and the influence of a series of large scale is often negligible on small ones, sometimes essential. In general, there is a misunderstanding of how to apply the characteristics of series of one scale to other scales.
The correctness of parameters by eye or by selection is sometimes essential for the result)))
https://3dnews.ru/1011653
I don't understand what's new, if the new ns was given the material of the old ns and it reproduced the rules and algorithm of the result of the old ns. Or did I miss something)))
I did not understand what is new, the new ns was given the material of the old ns and it reproduced the rules and the algorithm of the result of the old ns. Or did I miss something?)
As I understand it, the result is the written code of the new program, which reproduces the game without giving any new/any data input.
A unit root is the condition of finding the roots of a polynomial equal to (or less than) the modulus of unity. That the series is not wider than a certain corridor. At the edges the roots of the polynomial are equal to 1 or -1. If the roots are greater, the series becomes wider, if less, the series is in the corridor.
The concept of root (characteristic polynomial) is defined ONLY for autoregressive processes. There are reasons to consider any stationary process as autoregressive. There are also non-stationary autoregressive processes. But there are many more processes that are NOT stationary and are NOT autoregressive (and not reducible to them in any way) - for them the reasoning about roots makes no sense at all.
How can this be applied to how well the system describes the series.
This is a necessary condition (but not a sufficient one) and it only works within a given two-state assumption. If it is not satisfied, then it makes no sense to say that we are dealing with a series other than SB (the introduction of the second state turned out to be redundant - the price is always similar to SB). If it is fulfilled, then we need to check the normality and independence of the residuals, the significance of parameters differing from zero, etc.
In good sense, we should find a system with a minimum number of variables sufficiently correctly describing the series.
Well, yes, starting with their minimum and gradually increasing, realizing that at some point everything will be perfectly "described" due to overfitting from the abundance of parameters.