Are there other measures besides correlation that convey a similar kind of "moving together" concept? Aside from Fourier, a bit of filtering, a bit of wavelets, orthogonal polynomials, covariance, etc I haven't thought too much about time series analysis. I'm supposed to be giving a presentation on "unexpected correlations in markets/portfolios" in a couple of weeks and staring at a bunch of (exponentially weighted) correlation time series isn't too enlightening so far. Given the audience (equity+FI portfolio managers/analysts), I don't think they are necessarily referring to the mathematically precise definition of correlation and instead have something like Webster's definition in mind:
[quote]
Main Entry: cor·re·la·tion
Pronunciation: "kor-&-'lA-sh&n, "kär-
Function: noun
Etymology: Medieval Latin correlation-, correlatio, from Latin com- + relation-, relatio relation
1 : the state or relation of being correlated; specifically : a relation existing between phenomena or things or between mathematical or statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone [/quote]
Any ideas on how best to quantify that?
Thanks,
Eric
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i always come across "cointegration" w.r.t. time series and alternative notions of correlation. might be worth looking into, but not being a time series guy, i don't know anything about the concept.
Graeme gave some nice references on cointegration [url=/Show%20Post.aspx?PostIDKey=42247]here[/url].
I read enough to get the basic gist, but still no intuition yet. Thanks for reminding me I should look at cointegration again.
chiral3,
Higher cross moments sound scary to me too! I'll take a look. Thanks.
One day, in the midst of another one of his increasingly frequent homicidal fantasies, Croke noticed a new member had invaded his favorite forum. It was an obnoxious coed (or so he thought) who went by the nickname "Lilly". At first, all Croke could think about was strangling the life out of this giddy new member. Her insistent flirting with everyone was disgusting to Croke and he began a merciless vendetta against her.
He was sure that his prominent status would cause the other "regulars" to outcast the newcomer as he wished. On the contrary, everyone dug Lilly and even Croke's most vehement beratings fell on def ears. This infuriated Croke even more.
Depending on the application, there are a few ways to quantify the way things move together:
[list]
[*]covariance
[*]correlation
[*]cointegration
[*]spread (and the variance of the spread)
[/list]
Of these, the spread is by far the most intuitive and illustrative. There is nothing like being able to count something dollars to illustrate a concept.
Correlation is, with a bit of practice, also quite easy to understand. It's covariance scaled and has a nice boundary from [-1.0 1.0] (of course you know that). The important thing is that correlation illustrates linear dependence.
A very intuitive way to think about correlation (and I never hear this brought up) is simply this: correlation^2 is simply the R^2 value in a linear regression. So Sqrt(R^2) multiplied by sign(slope of regression line) equals correlation: Easy and very illustrative.
So, understanding linear regression is a good way to get a handle on correlation.
Hm... what else. Oh yeah, covariance:
One way to think of covariance is of correlation unscaled (note circular reference with above Smiley ). By itself, I don't think there is anything intuitive to understand about covariance. Best way to think of it is correlation with the scaling removed (I think anyway. I'd love to know if someone has a mental image that helps up his sleeve here).
Cointegration - don't think there is an easy way to illustrate it.
If you want a simple way to discuss correlation, all you really need to do is get everyone on board with covariance, then make the jump. DAX's R^2 approach will have the statistitians squirming in their seats (I know, I have used the same approach only to get into a long winded discussion about how R^2 can mislead if it is the only indicator being used, not in the presence of graphical depictions, etc. etc.)
My intuition about cointegration is this: Take two time series. You know that running a linear regression on one against the other is probably not meaningful, but do it anyway. Look at the time series of residuals. If it's stationary, the two series are cointegrated.
I'm not an econometrician, though, so this explanation is probably all messed up.
A Measure of Comovement for Economic Variables: Theory and Empirics
One day, in the midst of another one of his increasingly frequent homicidal fantasies, Croke noticed a new member had invaded his favorite forum. It was an obnoxious coed (or so he thought) who went by the nickname "Lilly". At first, all Croke could think about was strangling the life out of this giddy new member. Her insistent flirting with everyone was disgusting to Croke and he began a merciless vendetta against her.
He was sure that his prominent status would cause the other "regulars" to outcast the newcomer as he wished. On the contrary, everyone dug Lilly and even Croke's most vehement beratings fell on def ears. This infuriated Croke even more.
