# Tag Info

10

The PCA analysis does not really tell you what the bonds do but it tells you how the rates move together. The variations of $n$ rates (i.e. 1 y, 2y, ...) are split up in (at first) abstract factors like $$\Delta R_i = \sum_{j=1}^n e_{i,j} f_j$$ where $\Delta R_i$ is the change in the rate $i$ and $f_j$ is factor $j$ and $e_{i,j}$ is the (factor loading=) ...

4

I think an extremely interesting strand of research on this topic is represented by extensions of vine copulas with time-varying parameters. For vine copulas in general have a look at this site from the Technische Universität München: Vine Copula Models One of their research projects, which is the most relevant in this context, is:Time varying vine copula ...

4

The given matrix can not represent a covariance matrix since it would imply that asset 1 is negatively correlated to asset 2 and asset 3. But asset 2 is negatively correlated to asset 3 which contradicts the first statement. In general a covariance matrix has to be positive semi-definite and symmetric, and conversely every positive semi-definite symmetric ...

3

There are many techniques, but I would begin with Stambaugh Analyzing Investments Whose Histories Differ in Lengths. The full information maximum likelihood approach he describes basically involves regressing the short history series against the long history series to obtain the covariance with the longer history securities and adding back the covariance of ...

3

The Newey-West procedure is meant to adjust the covariance matrix of the parameters to account for autocorrelation and heteroskedasticity. It is typically used in financial applications when one estimates the alpha (a parameter in a regression model) of a portfolio or strategy. One would adjust the standard errors using the Newey-West procedure in order to ...

2

The answer of user27915816 led me into the right direction, yet I think I found an even better generalization: Distance Correlation (dCor) There are several reasons for that: It generalizes classical (i.e. linear) correlation in the sense that linearity is a special case. It gives identical readings for linear dependence. There are analogs for variance, ...

2

Mutual information measures how much knowing one variable reduces uncertainty about another variable. It considers any type of dependency (linear or non-linear), it's measured in bits, and it is widely used in machine learning, computer vision NLP and other fields.

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My answer will be very non-quantitative but the resulting models are actually quite mathematical but I like to stick to a general overview because of the proprietary nature of those models. Here couple thoughts though: You can't just try to explain market moves by a few indicators or a single Fed speech (by the way, the market hugely misread those ...

1

@pyCthon's comment hit home. So I did some tests. I compared a parametric computation to a Monte Carlo computation of IR Vol for a small set of fixed income securities. I was particularly concerned whether I could identify factors that would indicate that the difference would exceed 10% of the MC result. Here's are my summary findings: Vanilla IR ...

1

I have written R code for some time-varying bivariate fat-tailed copula functions (ripped off Patton's Matlab code) and played around with various optimizers. You can then use Rsolnp, nloptr, alabama or DEoptim packages to find an optimisation solution. Here is some R code where I play around with different optimisation algorithms. Note that the data2.csv ...

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