Thoughts on some of the absurdity of multi-currency analysis. - page 28
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In a set of BPs, it makes sense to talk about indices when they are independent BPs - orthogonal basis - zero correlation (Pearson's favourite) between BPs.
In practice, of course, there will be no zero correlation.
This is exactly what I have done. Although there are 8 working currencies, 18 currencies are used to calculate indices. In my opinion the result is quite close to orthogonality. If it's not enough, I will add more.
In general, I cannot call them indices, because everyone is presented with a stupid dollar index, which is not suitable for analysis, so I just call them currencies.
Of course, the initial set of BPs must be normalised. The easiest way to do this is to logarithm all price VRs and zero out their mean (by some pre-selected window size). Further I speak only about normalized price BPs.
Obviously, among the set of price VRs one can always take the majors as a basis, since all price VRs can be expressed through them by a linear combination. Of course, there can be many bases. For example, USD majors or JPY "majors".
I.e. the indices can be all the same majors. But the correlation between them is far from minimal. Thus, we must determine the eigenvectors from the matrix of the majors that are orthogonal by definition. They can be called indices.
Nah, I'm against normalisation, logarithm and all kinds of non-linearity. We don't need to do anything with the average, because we are not interested in the average itself. We're trading the difference, so knowing the relative change is sufficient. I put a reference point where all currencies are 1, on the vertical scale the relative change as a percentage.
I am prepared to argue the logarithm of the argument. But first I would like to understand what you are doing.
Can you explain without general words, but as a technician to a technician?
There seems to be nothing more to explain...
At the point where the vertical line is, all currencies are simply equated to USD=EUR=GBP=JPY=CHF=CAD=AUD=NZD=1.0 (i.e. 0.0% change). On each bar we calculate the percentage change of each currency and draw a point. I cannot show you how it is calculated. We calculate on the basis of the orthogonality requirement for the currencies.
I am prepared to argue the logarithm.
I, too, am prepared to argue for logarithm.
But "zeroing out the average" seems to be shamanism, and unreasonable at that. And I strongly disagree about singling out an orthogonal vector system. On the contrary, any detection of stable correlations (or regularities in correlation changes) is useful and tradable information which one should not get rid of but feed on. I.e. non-orthogonality (in this particular case) is our friend and breadwinner, but not a "coordinate system defect".
At each bar, count how much each currency has changed by and draw a point.
That's why I was talking about the logarithm of price BPs - as a simple transition from absolute changes to relative changes. But not the point.
We calculate from the requirement of orthogonality of currencies.
I am familiar with such an approach in the well known cluster indicators.
By orthogonality requirements do you mean the minimum correlation between BP of the obtained indices?
Do I correctly understand that IND_AUD / IND_USD = AUD/USD at each point?
If you have the grail, certainly not worth sharing. If not, why not discuss it substantively and without the flooding that is so beloved on this resource.
On the contrary - any finding of stable correlations (or patterns in correlation changes) I find useful and tradable information to be fed rather than disposed of.
There is no getting rid of correlations in an orthogonal system. Only getting rid of correlation illusions. Do you see correlation of JPY and CHF to the right of the vertical line? Then trade, no one is preventing you from doing so.
But "zeroing out the average" seems to be a shamanism, and an unwise one at that.
Prologarithm GOLD/USD and EUR/USD. How can we further compare the obtained BPs without zeroing the average?
And I strongly disagree about the orthogonal vector system. On the contrary, I consider any detection of stable correlations (or regularities in correlation changes) to be useful and tradable information that should be exploited rather than disposed of. I.e. non-orthogonality (in this particular case) is our friend and breadwinner, but not a "coordinate system defect".
Do I understand correctly that IND_AUD / IND_USD = AUD/USD at each point?
Exactly, except for minor deviations due to spreads and digital noise.
Not a grail, but something close to the limit of technical analysis. I'm going to make a robot out of this, digital filters and a few other things.