On "stationarity"...
When we talk about something being "stationary" we mean that the observations look like they could be drawn from the same "bag of observations" (distribution), regardless of what time we choose to look at.
1/5
When we talk about something being "stationary" we mean that the observations look like they could be drawn from the same "bag of observations" (distribution), regardless of what time we choose to look at.
1/5
https://twitter.com/TimmiHendricks/status/1369313259640283142
You can observe this by eyeballing charts.
VIX (blue) stays within a range the whole time. If it gets to extreme values, it's likely to revert back to moderate values.
By contrast, the SPX price (orange) just seems to drift away. It doesn't appear anchored to any range.
2/5
VIX (blue) stays within a range the whole time. If it gets to extreme values, it's likely to revert back to moderate values.
By contrast, the SPX price (orange) just seems to drift away. It doesn't appear anchored to any range.
2/5
We can also see this by sampling from the distributions at different times.
Let's divide our sample roughly in half (2004-2012 vs 2013-2021).
From the histogram, it's clear that SPX prices are not drawn from the same distribution in the first and second periods
3/5
Let's divide our sample roughly in half (2004-2012 vs 2013-2021).
From the histogram, it's clear that SPX prices are not drawn from the same distribution in the first and second periods
3/5
Compare this with the same plot for VIX...
It's much less clear that the VIX index marks are picked from a different distribution in the first and second halves...
4/5
It's much less clear that the VIX index marks are picked from a different distribution in the first and second halves...
4/5
To complete the discussion, let's look at the distribution of SPX log returns in a similar way...
After transforming the prices to log returns, it is now much less clear that they are picked from different distributions.
This is why we did it in the initial analysis.
5/5
After transforming the prices to log returns, it is now much less clear that they are picked from different distributions.
This is why we did it in the initial analysis.
5/5
Here's the original thread:
https://twitter.com/therobotjames/status/1369204237092093952?s=20
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