# Tag Info

## Hot answers tagged principal-components

6

One of the best pieces ever written on this topic is Salomon's "Principles of Principal Components," which is readily available on the Internet. I won't go into the details, since this paper is ridiculously comprehensive, but the fundamental idea is straightforward -- if you run a PCA based on yields, the first three components capture most of the variances, ...

6

It is preferable to use constant maturity yields (ideally par yields) for running PCA analyses. Using constant maturity par yields has several advantages: By definition, the yields are of constant maturity, so your results won't be distorted by "rolls." When you use either rolling futures yields or on-the-run bond yields, there could be many breaks in the ...

4

This is an interesting exercise and would be compelled to see the results of your data gathering. The principal purpose of treasury note (cash bond) analysis is for yields and the cross-asset class relative valuation where both provide signals. Alternatively, futures provide a technical analysis picture supplementary to yield dynamics. Personally I would ...

4

You can see my remark above for some more words on PCA for the yield curve and an interesting paper. About the question whether it helps us to creat a risk model: PCA on the yield curve changes (!) tells us: what are dominant moves (it turn out it is a pralell-shift, steepening and curvature change)? This gives us a picture and language to think and speak ...

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We can calculate the principal components by finding the eigenvalues and eigenvectors of the covariance matrix. The largest eigenvalue represents the largest variance, second largest eigenvalue the second largest variance etc. By plotting the components of the eigenvectors we can identify them with, e.g., shifts, tilts, flexing and so on. For example for a ...

3

To put things in context, if $\{{\bf X}_i\}_{i=1}^n$ is a set of variables and $\{{\bf Y}_j\}_{j=1}^n$ denote the principal components of ${\bf X}$ then $${\bf X}_j = \mu_j + \sum_{k=1}^n{\bf Y}_k A_{jk} \tag{1}$$ where $\mu = \mathbb{E}[{\bf X}]$ and $A$ is the diagonal representation of the correlation matrix $\Sigma = \mathbb{C}{\rm ov}[{\bf X}]$. The ...

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Don't be afraid to use one row in your spreadsheet for each day. Enter the date in column A, then increment the date by 1 day for each row until you reach the end of 10 years. In column B enter the formula "=YEAR(A1)" A1 being the cell with the date in it. Then calculate your principal and interest amounts based on the interest rate divided by the total ...

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A PCA explains the variation in data. A slope PC is usually identified by the pattern of the signs of the loadings. If the loadings of short term contracts have the same sign which is different from the sign of the loading of longer term contracts then such a PC is identified as slope PC. It means that if this PC goes up or down it affects short term ...

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I liked the following introductions to Partial LS Discriminant Analysis:  Partial Least Squares for Discrimination A Beginner’s Guide to Partial Least Squares Analysis Here some references to examples: XLStat Spreadsheet (you may need to install the trial to run the full analysis in Excel) R Package plsDA {DiscriMiner} R Package Muma

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I don't think that PCA works how you think it does. In coming up with orthogonal vectors (i.e. the eigenvectors of the covariance matrix), Principal Component Analysis generally ends up with each component as a linear combination of your original assets. So while you are reducing the dimension, it doesn't necessarily mean that you end up with fewer assets in ...

1

I browsed through the work and this is what I see: the lhs $r_{t+1} + \cdots + r_{t+H}$ is the sum of log-returns after $t$. the rhs is indexed by $t-i, i=0, \ldots, H$ thus this has something to do with the past before (and at) $t$. Thus the regression models the future ($r_{t+1} + \cdots + r_{t+H}$) dependent of the past where only PCA projections of ...

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In the case of N components: compute the NxN covariance matrix compute the N eiggenvectors and take the one that has the signs that you want the weights of this eiggen vector corresponds to the basket of N components that you wish to create

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In addition to the references already given by Matt I would recommend the following presentation which gives a good overview of the big picture, intuition and some mathematical background: http://zoo.cs.yale.edu/classes/cs445/slides/Pfizer_Yale_Version.ppt‎ See esp. pages 71ff. and 206ff.

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