Obtaining a stationary BP from a price BP - page 18
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What do you mean? What mistakes?
It's much simpler, because no matter how you twist and turn it, you can't get perfect stationarity. By definition, a stationary BP is a series, on which if we apply Bolinger Bands we obtain three strictly horizontal lines. I.e., neither a simple moving average (expectation) must not bend, nor channels (RMS) must not narrow - go away.
It is not so in theory or in practice. But I will not torture you with nerdiness)))) Just don't confuse the estimation of Mo and variance on the sliding window (which is what BB actually does) and Mo and variance itself as understood in nerd probability theory. But all BB lines on a stationary series will fluctuate within a fairly wide range, depending on the period of the BB calculation and the magnitude of the variance. And in the limit of infinity))) the BB period will converge to its mo and variance.
At a glance, what are the main parameters by which you can tell if this is the case, the trend?
No question. - Positive correlation coefficient between neighbouring samples in a series of first price differences.
This estimation can be done on all kinds of TFs and we will see that the coefficient is negative (as a rule), which indicates the "rolling" nature of the market. By the way, the last property is the most natural and indicates not the herd character of pricing, but rather a purposeful policy of central banks, which thus stabilise prices, thus allowing the national economy to develop more effectively.
The same result can be obtained by examining the distribution of the lengths of PZ. For an integrated CB (which MO, equals 0), the average length of a side of PP equals 2H, where H is a parameter for the construction of PP. For a rolling market this value is <2H, for a trending market >2H, and for a real market it is <2H on all trading horizons (almost always).
I want to emphasise again, THEN, if it did price in forex, it would cause a herd effect or in other words, define the Market as trending. Which is not the case, and thank goodness for that. The price in the Market is not shaped by speculators or even Big Speculators, but by the economic policy of the state, aimed primarily at stabilising the exchange rate of the national currency.
No question. - Positive correlation coefficient between neighbouring samples in a series of first price differences.
This estimation can be done on all kinds of TFs and we will see that the coefficient is negative (as a rule), which indicates the "rolling" nature of the market. By the way, the last property is the most natural and indicates not the herd character of pricing, but rather a purposeful policy of central banks, which thus stabilise prices, allowing the national economy to develop more effectively.
I see. There is nothing to be caught with that definition - I agree. The problem, as I suggested, is your way of defining the trend. I.e. technically you are right, if you take BP as a whole. But the trick is that not all plots can be considered for trend definition at all . Here again I come back to defining plots with local stationarity by quasi-stationary processes.
The same result can be obtained by examining the distribution of the lengths of PZ. For an integrated CB (which MO, equals 0), the average length of a side of PP equals 2H, where H is a parameter for the construction of PP. For a rolling market this value is <2H, for a trending market >2H, and for a real market it is <2H for all trading horizons (almost always).
I can't say anything.
I want to emphasise again, TOLPA, if it did price in forex, would cause a herd effect or in other words define the Market as trending. Which is not the case, and thank goodness for that. The price in the Market is not shaped by speculators or even Big Speculators, but by the economic policy of the state, aimed primarily at stabilising the exchange rate of the national currency.
Not sure about the "crowd" - I mean the conclusions. However, it does not matter in this context.
But the point is that not all plots can be considered for trend detection at all . Here I go back to defining plots with local stationarity by quasi-stationary processes.
And I agree with you.
Here, as well as everywhere else in this World, the uncertainty principle works - the more exact we try to define something by one parameter, the more error we have to accept by another one. Striving for smaller temporal localization of the process of interest, we will invariably decrease the reliability of the result obtained (due to insufficient statistics), and vice versa - increasing the size of the sliding window, we start involuntarily integrating phenomena different in nature, thus reducing the value of the obtained result. There must be a golden mean and I doubt it can be determined analytically from general considerations. This is precisely the case that obliges us to conduct a forward analysis and analyse each particular result, thus building a consistent picture of the phenomenon.
I see. There's nothing to catch with that definition - I agree. The problem, as I suggested, is in your way of defining the trend. I.e. technically you are right, if you take BP as a whole. But the trick is that not all plots can be considered for trend definition at all .
>> Yes, that's exactly right.
Neutron, you're talking about the series as a whole, and I'm only talking about some of the highlights. I have also seen a return (antipersistence) in my recent experiments with dummies (the percentile of the dummy return and price is much greater than that for trend continuation - especially on dummies with small periods). But it's precisely the global reversion which is of no use: it should also be observed on a normal Wiener process.
My acerbic angel in the form of The Oak Theorem never lags behind me.
A stationary time series has a maximum and minimum in its values, so the graph of a stationary BP lies in a strictly horizontal corridor. It can be divided into two types:
You are confused. The term stationarity means the stationarity of the moments of the series of the first price difference. And the price itself is obtained by integrating (summing up) the counts of this SV. In this case it will not lie in a strictly horizontal corridor.
On the left is the SP with MO=0 (analog of the first price difference series on the selected timeframe), on the right - the integral of this SP (analog of the price series). As you see, it does not lie in the corridor, although the process that generates it is stationary in the strict sense.
Yes, exactly.
But it is precisely the global persistence which is of no use: it should also be observed on an ordinary Wiener process.
Yes, wait a minute.
In the figure on the right I have exactly the usual Wiener process (one-dimensional Brownian wandering without drift) and it is neither globally persistent nor antipersistent - it is neutral to 1/SQRT(from the number of counts).
What did you, Alexei, mean by that?
You are confused. By stationarity, we mean the stationarity of the moments of the series of the first price difference. And the price itself is obtained by integrating (summing up) the counts of this SV. In this case it will not lie in a strictly horizontal corridor.
On the left is the SP with MO=0 (analog of the first price difference series on the selected timeframe), on the right - the integral of this SP (analog of the price series). As you see, it does not lie within the corridor, though the process that generates it is stationary in the strict sense.
What am I confused about? As I said, the price series is not stationary, but its first differences are. And those differences belong to the second kind of stationary process, according to my invented definitions, because they contain dependence on previous values. :)