Obtaining a stationary BP from a price BP - page 22
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For a cumulative sum the variance increases in direct proportion to the square of time.
For a stationary VR the variance = const
Intuitively, we associate the stationarity of a time series with the requirement that it has a constant mean and fluctuates around this mean with a constant variance.
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A series x(t) is called strictly stationary (or stationary in the narrow sense) if the joint probability distribution of m observations x(t1),x(t2),:,x(tm) is the same as for m observations
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In other words, the properties of a strictly stationary time series do not change when we change the origin.
Mathematical expectation Mx(t)=a
Dispersion Dx(t)=M(x(t)-a)2= c^2
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A series x(t) is called weakly stationary (or stationary in the broad sense) if its mean and variance are independent of t.
Qualitatively, a stationary series is a series in statistical equilibrium, in the sense that it does not contain any trends (it is a sideways trend with clear boundaries), whereas a non-stationary series is such that its properties change with time
Colleagues, I apologise for the mistake (thanks to Sergei for the subtle hint :o). Was just calculating a tricky transformation that was the input to the difurcation, and this was implemented in one algorithm.
Row:
Sort of autocorrelation (R(n)=R(-n)):
Estimate (of course, there is an error in the calculation)
Incidentally, one common way of identifying AR/ARIMA models is to predict backwards. It can be seen that this does not work for such series.
And stationary VR has dispersion = const
of course. But we are talking about cumulative sum ;)
Can we keep it simple...
there's a "chewy" pound-frank discussion going on here.
Any specifics from the applicants?
That's not for grasn.
;)
Of course. But it's about the cumulative amount ;)
And I'm talking about stationary rows. I didn't even mention these very sums.
If the cumulative white noise deviates from MO by two sigmas, with 97.5% probability it will return there again regardless of sampling frequency, be it ticks or owls. For example we may enter at one sigma, there will be more trades, but the probability of return will be 67%, and in 33% of cases it will go to two or three sigmas.In fact if a stationary process deflects even by how much from MO it will return to its MO with 100% probability,because this is the "fair price" of this process.This is a kind of attractor attracts all sorts of non-linear dynamical systems lovers.
Sorry, but you are writing nonsense, which in turn shows a complete lack of mastery of the material.
I can't add anything to what Avals said correctly:
Avals wrote(a) >> The increments are independent and nothing should go back anywhere. How does the cumulative sum return to mo? Take an SB with increments with mo=0 - it can deviate as far from zero as you like and not return to it for as long as you like. The cumulative sum has a variance that increases in direct proportion to the square of time.
grasn wrote >>
There's a deep philosophy here. What is primary, the prediction model and consequently the construction of the TS on its basis or the TS for which the prediction is selected. >> So far I don't really understand, what "optimal" TS means (on what range, among what this optimum is), why only one step forward is important for it, how it correlates with spread.
Let us have an arbitrary TS that trades according to the most general algorithm.
Analysis unit:
1. Determines the entry point into the market and direction of the open position;
2. determines the exit point, i.e. closing of an open position.
It is clear that when defining the trading algorithm in such a way, we break down the price TP into time-isolated sections, where we are in the market. Let's call the TS optimality parameter - k the ratio of the number of payments of DC commissions to the number of completed transactions. In this case it is evident that k=1 always and the series of transactions contains any long unidirectional series. We will call an "optimal" TS the one that minimizes the parameter k.
It turns out that there's no need to close and open one-directional consecutive positions losing the spread at each step. Consecutive unidirectional transactions can be combined by "not exiting" the market and losing one spread at each "virtual" transaction series instead of each series member that will lead to minimization of the optimization parameter. Now k<=1.
Such an TS, all other conditions being equal (when one and the same analytical control unit works for different TS), will give the maximum possible return defined as points per one transaction (on average) and will be optimal in the stated sense.
Now, if you turn on your "artistic" imagination, you can see in front of your eyes a flipping TS that is always in the market. Which is what was needed to prove.
Sorry, but that's not true again. The increments are independent and nothing should go back anywhere. How does the cumulative sum return to mo? Take SB with increments with mo=0 - it can deviate from zero as far as it wants and not return to it as long as it wants. The cumulative sum has a variance that increases in direct proportion to the square of time.
White noise is also not time correlated - this is its main condition - but its variance is finite. For example, the first difference in SB is noise.The cumulative sum of these differences is random walk, all right.Now take two or more highly correlated series (SB - cum. sum), do a regression analysis and get the residuals (white noise - cum. sum).
"Live and learn," thought the Lieutenant, moving the silver cigarette case from his trouser pocket under his pillow.
Do you know what your problem is? Nor do I know. But you do have one.
What the hell are you doing? You're trying to fuck a spherical horse. Well, love and advice. And more kids...
===
By golly, Niroba's branch is out.
"Live and learn," thought the Lieutenant, moving the silver cigarette case from his trouser pocket under his pillow.
Do you know what your problem is? Nor do I know. But you do have one.
What the hell are you doing? You're trying to fuck a spherical horse. Well, love and advice. And more kids...
===
By golly, the Niroba branch is resting.
once again I could not contain my delight at the inquisitiveness of your mind.
But my immature mind still can't accept your 300longitudesWhat the hell are you doing? You're trying to fuck the spherical horse. Well, love and advice.
>>Peter, finish your humpbacked excuses and hurry up and join us in this feast of life - get to work!)