Machine learning in trading: theory, models, practice and algo-trading - page 1014
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I will not tire of quoting excerpts from Kolmogorov:
In other words, the following are considered:
1. Returns
2. the ACF for returns.
If the ACF satisfies the following condition:
then such a discrete returnee series is predictable.
That is all.
There are no other predictors, have not been and will not be.
Where does the ACF of price increments come from? They are obviously non-stationary and the covariance function will depend on two variables: B=B(t,k) and you simply do not have enough data to calculate it.
Where does the ACF of the price increments come from? They are obviously non-stationary and the covariance function will depend on two variables: B=B(t,k) and you simply do not have enough data to calculate it.
The ACF that is shown in the picture is the algorithm taken from ARIMA. It is calculated from the last n-bars.
The ACF algorithm in the picture is taken from ARIMA. It is counted by the last n-bars.
First of all, my comment was about inappropriate attaching Kolmogorov's article about stationary processes to obviously non-stationary case.
Although, ARIMA also reduces everything to stationarity, which can be true for prices only approximately and only on certain time intervals (e.g. one autoregressive coefficient during a trend, another one during a subsequent flat). We cannot predict when it is necessary to change the model and this is a consequence of non-stationarity.
First of all, my comment was about inappropriate attaching Kolmogorov's article about stationary processes to the obviously non-stationary case.
Although, ARIMA also reduces everything to stationarity, which can be true for prices only approximately and only at certain time intervals (for example, some autoregressive coefficients during a trend, while during a subsequent flat, quite different ones). We cannot predict when it is necessary to change the model and this is a consequence of non-stationarity.
+
What is meant by periodicity?
And as far as I know ACF is not just a sum of products. There is a much more complicated algorithm.
I stand by my opinion - ACF estimation for a discrete series of returnees is the sum of products of 2 consecutive returnees of sliding sampling.
About periodicity...
I think it's simpler this way:
Trade (predict the next return) when the current ACF value>0, i.e., when there is an obvious dependence of the increments, the so-called "memory".
I stand by my opinion - the ACF estimate for a discrete series of returnees is the sum of the products of 2 consecutive sliding-sample returnees.
About periodicity...
I think it's simpler this way:
Trade (predict the next retournee) when ACF>0, i.e., when there is an obvious dependence of the increments, the so-called "memory".
Look at the indicator, is it like that or should something be changed?
Look at the indicator, so or something to redo? The absolute value of the increments is still probably better to leave (minus multiplied by minus plus), then the minimum will only be 0.
Sorry, I can't. Busy looking for the Grail in diffusion processes. It's me - I help here as much as I can, because I believe in neural networks and forests.
Sorry, I can't. Busy searching for the Grail in diffusion processes. I'm helping out here as much as I can, because I believe in neural networks and forests.
Then I remove the indicator?
Then I remove the indicator?
Yes. You don't need an indicator. We need predictors by Kolmogorov. Otherwise it is impossible and it will take another 1000 pages to make me laugh.
I stand by my opinion - the ACF estimate for a discrete series of returnees is the sum of the products of 2 consecutive sliding-sample returnees.
About periodicity...
I think it's simpler this way:
Trade (predict the next returnee) when ACF>0, i.e., when there is an obvious dependence of the increments, the so-called "memory".
1) There is no ACF in unsteady processes. Read at least Orlov from your suggested collection of books about the moments of nonstationary processes.
2) The "memory" of nonstationary processes is not good either. It can be detected when it does not exist (a non-stationary process with independent increments) if we do calculations as for a stationary process. You can have it but it may be different at any moment and it is not clear what exactly the process "remembers" at that moment.