Whether there is a process whose analysis of one part does not allow predicting the next part. - page 7
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The wrong coin. The process is non-deterministic. I.e. a random series with a bevel.
We are essentially talking about the same thing. See the graphs of a coin wandering with a bevel (positive MO) just above. A prediction based on a commonly known MO is not a prediction, however, because relative to the target (the price level the process will reach due to its mix) itself is also uncertain. In the real world this is what happens: if, for example, this graph represents currency movements, its appreciation will increase the cost of borrowing and hence the swap difference will adjust the trend by the required amount and the series will again become chaotic without a clear trend.
In essence we are talking about the same thing
In essence it can be. But
1. Prediction is possible if there is a deterministic component.
That's a bit harsh. If there is a statistical advantage. And the nature of this advantage can only be judged by the course in a particular case.
Well, or yes, divide into trending and anti-trending.
The division into deterministic and stochastic trends seems to me to be a tricky one. What do we care if both of them (if they exist) may end literally at the next new candle and we can only judge about it when this candle becomes history. This is a dead end in trading. It may be important for analysis of the past (cardiogram for example), but nothing for forecasting.
The whole dog is buried in the ability to highlight the trend. Above I formulated the 1st requirement - differentiability on the right. The 2nd requirement: the residual after trend extraction must be stationary. I called the cubic spline for a reason. It seems to satisfy both conditions.
I attach here an article on trend extraction. I apologize for poor quality of the partial translation of the original text. I don't want to take the trouble.
joo:
Здрасте.
Предлагаю уважаемому сообществу придумать такой процесс, который нельзя прогнозировать (так, что бы на этом прогнозировании нельзя было делать деньги). При этом, что бы процесс не имел стационарных стат-характристик по времени.
faa1947:
Not stationary. By definition.
Bullshit.
The simplest example. Here is the process: x(t) = Acos(wt+fi), where A and w are constants and fi is a random phase uniformly distributed in the interval (-pi/2;pi/2). The non-stationarity of x(t) can be proved elementary - just calculate the ACF and see that it is not constant over time. But the process is quite predictable and quite stable. If one had been in the forex market, it would have been easy to make money.
Bullshit.
The simplest example. Here is the process: x(t) = Acos(wt+fi), where A and w are constants and fi is a random phase uniformly distributed in the interval (-pi/2;pi/2). The non-stationarity of x(t) can be proved elementary - just calculate the ACF and see that it is not constant over time. But the process is quite predictable and quite stable. If one had been in the forex market, it would have been easy to make money.
ACF proves nothing but trend and cycle. Detrend and discuss.
Have you read the definition of stationarity in the broad/narrow sense?
There are a million examples of non-stationary processes that are remarkably predictable, as well as equally many stationary processes that cannot be predicted. Once again, these things have nothing to do with each other.
The division into deterministic and stochastic trends seems to me to be a tricky one. What do we care if both of them (if they exist) may end literally on the next new candle and we can only judge about it when this candle becomes history. This is a dead end in trading. It may be important for past analysis (cardiogram for example), but nothing for prediction.
The point is that the probability of termination of deterministic trends/antitrends is less than/above 0.5, and we can already work with it. Stochastic trends cannot be handled. Learn to identify deterministic trends and skip the stochastic ones and you'll have a sweet treat.
Candy is very unhealthy.
The problem is residue and breaks. While the residuals can be dealt with (e.g. ARCH), the kinks are a problem.
There are a million examples of non-stationary processes that can be predicted brilliantly, as well as the same number of stationary processes that cannot be predicted. Once again, these things have nothing to do with each other.
This is news to me. A stationary series is predictable by definition - within a sko. An unsteady series has no sko - what is the prediction? But it's not just about sko.
Still, I would like to return to the problem of detrending.
What is being detrended?
Level? Straight line? Or curve? Or splines?
And what about phase? Do we detrend it too?
Is there just one trend or many? Maybe a wavelet?
So fixation on deterministic and stochastic trends for forecasting is a harmful thing, because it suggests to solve problems that the trader does not have.