<p>The goal is to reproduce this chart:</p>
<p><a href="https://i.sstatic.net/ffCA8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ffCA8.png" alt="enter image description here" /></a></p>
<p>I first looked at the legend. It reads: &quot;Correlation of Front and Back Fed Funds curve, Pivoted Around Peak Rate (Rolling 250 Day). Then I noticed that the Y-axis is in &quot;%&quot; which is a unit that I have not seen used for correlations. After all, it's a unitless measure, assuming we're talking about the rather axiomatic statistical form of &quot;correlation&quot;:</p>
<p><span class="math-container">$$ Cor = \frac{Cov_{xy}}{\sigma_x\sigma_y} $$</span></p>
<p>After a bit more contemplation I thought perhaps it's actually a rolling regression, given the 250 window. But if that was the case, then the y axis would be in beta space if I'm not mistaken (again not %).</p>
<h2>Question</h2>
<p>The good news is that yield curve data is in the public domain, so getting the high and low ends should be straight forward, the question is once I have daily time series for front/back of the curve for all those years, what do I do with it to get the chart as pictured above? By this I mean the calculation for the y-axis.</p>

CC BY-SA 4.0
2022-11-02T11:54:20.597Z
Correlations as defined statistically (covariance divided by product of standard deviations) must be between $-1$ and $+1$.  If you multiply these by $100\%$ then you would say they must be between $-100\%$ and $+100\%$.
Henry
CC BY-SA 4.0
2022-11-03T00:18:12.407Z
@Henry Ah, you're totally right. Now it makes some sense.
Arash Howaida
<regression><data><yield-curve>
How to calculate the correlation of yield curve extrema?
Arash Howaida
# How to calculate the correlation of yield curve extrema?

(Asked by: username_0 on 2022-11-02)

The goal is to reproduce this chart:

[![enter image description here](https://i.sstatic.net/ffCA8.png)](https://i.sstatic.net/ffCA8.png)

I first looked at the legend. It reads: "Correlation of Front and Back Fed Funds curve, Pivoted Around Peak Rate (Rolling 250 Day). Then I noticed that the Y-axis is in "%" which is a unit that I have not seen used for correlations. After all, it's a unitless measure, assuming we're talking about the rather axiomatic statistical form of "correlation":

$$ Cor = \frac{Cov\_{xy}}{\sigma\_x\sigma\_y} $$

After a bit more contemplation I thought perhaps it's actually a rolling regression, given the 250 window. But if that was the case, then the y axis would be in beta space if I'm not mistaken (again not %).

## Question

The good news is that yield curve data is in the public domain, so getting the high and low ends should be straight forward, the question is once I have daily time series for front/back of the curve for all those years, what do I do with it to get the chart as pictured above? By this I mean the calculation for the y-axis.

**Tags:** regression, data, yield-curve

> **Comments:**
> **username_1**: Correlations as defined statistically (covariance divided by product of standard deviations) must be between $-1$ and $+1$.  If you multiply these by $100\%$ then you would say they must be between $-100\%$ and $+100\%$.  
> **username_0**: @username_1 Ah, you're totally right. Now it makes some sense.  

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## 0 answers

