Quote from talontrading:
When you start going through old posts, please specifically respond to the items I highlighted in bold. This is disturbing coming from someone with a strong math background as it, frankly, is nonsense.
1. What is "lagging kurtosis"? This is not a meaningful term.
2. How do you generalize from skewness to the weight in the tails?
3. Is this assumption valid for distributions other than normal? How about for a distribution such as Cauchy with non-finite variance?
4. The normal distribution has a kurtosis of 3 and some software packages subtract 3 (wrongly) from kurtosis to give you excess kurtosis. Excel is one of those packages that does this, but in these packages a kurtosis of 0, not 1 as you state is normal. I can construct a multitude of leptokurtic distributions with heavy left tail risk that exhibit positive skewness so I do not understand the sense of what you're saying here.
5. And on a more philosophical level, do you really think skewness and kurtosis have any meaning for the complex distributions we see in actual trade returns? Aren't there better measures of tail risk? Why, aside from these stats being readily supplied (albeit with incorrect values (see earlier post)) by Excel's Data Analysis module, are you focusing on these and not at least doing a visual inspection of the histograms?
Please clarify the math behind these points when you get a chance because these concepts are so fundamental to understanding the mathematics of expectancy and chance. I'm not trying to be confrontational, but these issues must be addressed.
Per 1) Lagging Kurtosis is any kurtosis value below 1. It's not a normal description, but the best I could describe how you know there are fat tails in the distribution.
ex-post edit: Your other posts mention 0 being the normal kurt value, but I really swear I remember vividly a class where the instructor had to mention excel calculates kurtosis differently, and subtracts three, but as you see, I'm not sure why I thought 0. The memory is a little distorted. I'm still confident that 1 in excel is the measure of normal distribution.
Per 2) It's very obvious to me, if the skew is positve, it might be that there are "more peakedness" at the other end. Perhaps it will be more obvious to you if I present the graphical representation of the distribution. I think it's <b>extremely obvious as to where the skew is, and why there are fat tails at the positive end.</b> Just have a look at the enclosed chart, if you think otherwise, I'd need to re-think what I know about statistics.
Per 3)
http://en.wikipedia.org/wiki/Cauchy_distribution I don't believe this applies to anything but physics, and I don't really care to comment about it. <b>I would say any distribution of a financial dataset can be converted from non-covariance stationary <i>to covariance stationary through several transformations.</i> </b> I describe mine as a "normalized z-score", requiring probability theory to understand, and not much more. If you're good at statistics, you should know what I'm talking about.
Per 4) For some reason, I recall vaguely in a class that 1 in Excel was actually where the normal distribution laid from kurtosis. Mean of zero, sigma of 1 was a normal distribution. Maybe I'm just remembering or misinterpreting an old memory.
Per 5) The visual inspection confirms my analysis as well. Thank you for confirming it with the histogram below.
ex-post edit: While re-reading this post, I discovered, you maybe wanted a histogram. It's pretty obvious to me.
I just started. Please let me get through these posts, as there is a bit of dialogue I need to address.
