Correct calculation of currency indices. - page 19
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Metamathematics proves that any non-contradictory mathematical theory is a tautology (does not formally carry new information). Nevertheless, mathematics is a very useful discipline, although it is a servant of sciences :)
Your reasoning is pure sophistry, the proof of which is only in your head (if there is any).
The sciences are only interesting as an applied discipline that would be impossible without the theoretical one.
Well, applied mathematics is concerned with filtering information.
For example, there is a process and there is a lot of information (explicit or implicit), we model the process mathematically and get much less information, but the most important.
There were two apples added a third, in fact there were many cells (molecular structures) but having simplified the mathematical model we got a usable formula.
At the same time the magic of mathematics lies in the fact that the evolution of the system can be obtained not only by redundant information, but also by partial information.
Anyway, I've got enough of that, so let's move on...
Let's assume that indexes really exist, but they must exist if there are currencies :)
And we can calculate the missing dollar index. Isn't it great?
But what is the dollar index, we can see only by calculating the before and after correlations. We calculate correlations in, say, 10 samples by moving window between all instruments and then display the average correlation before and after the conversion (to avoid the influence of negative correlation we will sum the modules when calculating the average). Suppose the transformation has decreased the symbol correlation (I say "suppose", because I have long ago removed all calculations, but anyone can repeat them). And if the correlation has decreased, then the dollar index is nothing more than a common basis. But since the correlation is not disappeared, we can continue the calculation even more general basis (by introducing in the calculation have injections including the dollar index), and can continue this way for a long time, but the moment comes when the next index basis does not reduce the correlation, and increases it. That is, we have reached the limit. Thus, we have a huge amount of components, including the hardly correlated symbols that we habitually call currencies. The question arises: what should we do with them now? You cannot trade on these figures, though of course the conversion is reversible and you can always recalculate everything. Indexes are like a drunkard on a ship, it would be logical to extrapolate for some counts (because the result of any smoothing is lag, and indexes are useless figures without it) and shift the number of counts back to get the market condition. But here's the problem - there is still no method that precisely extrapolates market data. Bam, faint. The reason is that the market is not stationary, and all methods of extrapolation require the constancy of the obtained transformation coefficients. Thus, using the known extrapolation methods we will obtain (albeit similar) forecasts with huge errors. Calculating backward from all these bases and indexes we'll get error accumulation and total nonsense forecast. The reason why it is needed when the extrapolation of currency pairs themselves can be done with fewer errors.
If someone says "I do not need extrapolation, I trade on indices", but it is impossible to trade on noise, and if you smooth out the noise, you get delay, so what do you trade on? In short no matter how you look at it indexes don't give you an advantage over random entry. Amen.
I'm not talking about "evil", I'm talking about the derivative. Remember what the derivative is in the physical sense - just Δy = f(x0 + Δx) - f(x0) . We can't model the function of price movement over time, but we can measure the change in Δy at any point in time. There is a statement that the dollar is the most valued and it is the dollar that makes the majors move, i.e. the euro itself or the pound relative to the dollar have a small price movement. So: it makes no difference how indices are calculated, but when multiplying two random variables (say EURUSD * GBPUSD) we get the mathematical expectation for the dollar - i.e. the average value of the dollar price at that moment in time. For trading, the knowledge of some real value of the dollar has no practical value, but if you control the increase of the dollar's value Δy over time, you may decide whether to buy or sell USD.
ZZY: try to analyze the behavior of deviations of increments of indices (∑Δy) / Δy
Let us get on with it.
--
I divide currency (and other asset) indices into "clean" and "dirty" (; unclean ;).
"Unclean" more often than not claim to bemore useful for trading (which I highly doubt, for the authors more often than not just don't know how to count pure indices). ;-)
So, net indices.
The problem statement is simple: To derive formulas to calculate some floating values (called asset indices) that satisfy the condition of complete consistency with the rest of the basket indices and their traded relations (trading instruments) at any given time. In other words (in terms of currencies): the ratio of one index (say USDx) to another (say EURx) must match the rate of their traded relation (i.e. EURUSD) at any time. Ah yes, the basket. We cannot derive such formulas unless we first fix a set of instruments (currencies and pairs). Such a fixed set is called a basket.
For example, let's derive formulas for a set of instruments that includes all currency pairs between [USD, EUR, GBP, JPY and CHF]. Five currencies (in this case), but there can be as many and as many as needed, provided there is enough information for their construction (i.e. all exchange rates of corresponding currency pairs are known or can be derived from known ones).
For this purpose let's build the following matrix:
Consider the rows of this matrix. In each row we have a set of currency pairs (or their inverse values easily obtained from pairs) and one unit (like CHFCHF or EUREUR).
If we multiply all elements of each line, the result will be fractions of the form XXX^5 / (USD*EUR*GBP*JPY*CHF). It is principally important for us that all these fractions have the same denominator (I call it the basket denominator). In the numerator of all these fractions, the same currency is multiplied by itself five times (the number of currencies in the basket). If we calculate the fifth (for a given basket) power from these values, the currency in the numerator will return to the first power, and the geometric mean of all currencies in the basket will appear in the denominator. As it was mentioned above, this value is the same for all the fractions, and that is why the obtained values have the property that when divided by one, after the reduction of denominators they guarantee the equality of the obtained ratio to the corresponding currency pair at any moment of time.
The problem is solved. The formula is derived and justified.
--
Those who understood the reasoning can easily understand the simple mathematical fact that the calculation of the net indexes cannot be done differently (a variation-optimization method is not another way) and cannot lead to other values (to the exact multiplier of the denominator).
Amen.
I hope the topic can finally be closed.
Although it is of course possible to wallow in some "dirt". :) It would only take a reasonable justification.
Another numbers game, which makes no sense, nor does it take into account the existing practice of index construction.
The point: economic (consideration of weights taken from the economy) + behavioural (believe in the correctness of Dow Jones, where you add and divide).
Usually both senses exist in all indices.
In the new indices, for example the RTS MICEX, very recently component weights were taken into account. The economic sense was embedded in those weights.
Another numbers player.
Assuming that indexes really exist, they must exist if there are currencies :)
.................
no matter how you spin it, indices don't give you an advantage over random entry. Amen.
The darkness of delusion and the inability and unwillingness to rise above the vanity.
1. No noise in the market.
2. No filtering delays that would interfere with trading. Or by delay you mean something that has nothing to do with delay.
3. there is such a thing - spectral analysis. Solves all the problems of "darkness".
4. The derivative has already been written about.
5. The market is stable by its changes. Hence, you have to look for them. This is an advantage.
SZY: try analysing the behaviour of index incremental deviations (∑Δy) / Δy
Another numbers game, which makes no sense whatsoever and takes no account of existing index construction practices.
The point: economic (accounting for weights taken from economics) + behavioural (believing the Dow Jones is correct, where you add and divide).
Usually both senses exist in all indices.
In the new indices, for example, the RTS MICEX, very recently component weights were taken into account. These weights included the economic sense.
Another numbers player.
Poor bastard. :(
Get well faa1947.
hmm, and how to build a function for a stochastic process? although I have successfully forgotten higher mathematics, but there was a topic on the forum and google suggests that it may be the Monte Carlo method, although I think it will turn out to be another self-deception, like fractal drawings of a fern leaf - it looks similar, but nature never repeats itself by copying - there are always inaccuracies.
imho, if one is to use indices to build a TS, then it is sufficient to consider, as I said, the index itself as a derivative of the movement of currency, then one only needs to work out the procedure when the sign of the increment +Δy changes to - Δy, and when Δy goes beyond some measurement limit, i.e. measuring the acceleration
Let's assume that indexes do exist, but they must exist if we have currencies :)
And we can calculate the missing dollar index. Isn't it great?
But what is the dollar index, we can see only by calculating the before and after correlations. We calculate correlations in, say, 10 samples by moving window between all instruments and then display the average correlation before and after the conversion (to avoid the influence of negative correlation we will sum the modules when calculating the average). Suppose the transformation has decreased the symbol correlation (I say "suppose", because I have long ago removed all calculations, but anyone can repeat them). And if the correlation has decreased, then the dollar index is nothing more than a common basis. But since the correlation is not disappeared, we can continue the calculation even more general basis (introducing in the calculation have injections including the dollar index), and can continue this way for a long time, but the moment comes when the next index basis does not reduce the correlation, and increases it. That is, we have reached the limit. Thus, we have a huge amount of components, including the hardly correlated symbols that we habitually call currencies. The question arises: what should we do with them now? You cannot trade on these figures, though of course the conversion is reversible and you can always recalculate everything. Indexes are like a drunkard on a ship, it would be logical to extrapolate for some counts (because the result of any smoothing is lag, and indexes are useless figures without it) and shift a number of counts back to get the market condition. But here's the problem - there is still no method that precisely extrapolates market data. Bam, faint. The reason is that the market is not stationary, and all methods of extrapolation require the constancy of the obtained transformation coefficients. Thus, using the known extrapolation methods we will obtain (albeit similar) forecasts with huge errors. Calculating backward from all these bases and indexes we'll get error accumulation and total nonsense forecast. The reason why it is needed when the extrapolation of currency pairs themselves can be done with fewer errors.
If someone says "I do not need extrapolation, I trade on indices", but it is impossible to trade on noise, and if you smooth out the noise, you get delay, so what do you trade on? In short no matter how you look at it indexes don't give you an advantage over random entry. Amen.
Finally someone has written something sensible about indexes. Although only the top half of the text makes sense, but that's a good thing.
Let's leave extrapolations and predictions alone, and look at the history, because I am always amazed by people who expect good results in real time from the indicator, which cannot correctly describe the history.
Let's look at 2 pairs on the same time frame.
Both show a trend, both take up the whole screen, how to choose the best one?
One look at the indices is enough to make a choice. There are many traders who have never even thought about choosing a currency pair. Probably they do not need indexes, they can just sit on Eurobucks forever.
Extrapolation of indices is a separate topic. Yes, there are no well-known methods for such extrapolation. Do they exist for currency pairs? Neither do they. Then what is the difference?
That poor bastard. :(
Get well faa1947.
...
Extrapolation of indices is a separate topic. Yes, there are no generally known methods for such extrapolation. Do they exist for currency pairs? Neither do they. Then what is the difference?
The difference is that the quote extrapolation will process one series, and the index extrapolation will process several series, but in this case we trade in pairs and therefore for making a trading decision we will have to recalculate the forecast of indexes into pairs and this means that the errors will sum up and as a consequence the errors are higher than in the case of pair extrapolation.
...
One look at the indices is enough to make a choice. There are many traders who have never thought of choosing a currency pair. Probably they do not need indexes, they can just sit on Eurobucks forever.
Well, let's deal with this extrapolation, as they say, let's solve problems as they arise...
What I see in the screenshot: I see a lot of noisy information, may be it's visually clear where pairs are moving (though not the fact), but it says only that the human brain could process (to smooth noise), programmatically the direction signal is much more difficult, I will have to smooth the series, and most smoothing methods inevitably make a lag. So the agenda is this.
First of all, we should find a lag-free smoothing method and then decide on the decomposition of quotes into indexes. Suppose there is such a method.
Then the following conclusion is logical: if we have the method of non-delayed smoothing, then why do we need indexes?