I am struggling to prove that for a normally distributed loss RV introducing stochastic volatility (\sigma_1 with probability 0.5 and \sigma_2 with probability 0.5) would make kurtosis bigger than 3 (fat tails).
Can someone help?
Kurtosis is the standardized fourth central moment and is a measure of tail density; e.g., heavy or fat-tails. Heavy-tailedness also tends to correspond to high peakedness. Excess kurtosis (aka, leptokurtosis) is given by (kurtosis-3). We subtract three because the normal distribution has...
Learning objectives: Describe the four central moments of a statistical variable or distribution: mean, variance, skewness, and kurtosis. Interpret the skewness and kurtosis of a statistical distribution, and interpret the concepts of coskewness and cokurtosis. Describe and interpret the best...
In the 2011 quant part a video you define the numerator of skewness as E[(Y-mu)^3] and then as mu^3 (slide 14). The same goes for kurtosis. Is there an error or am I interpreting something incorrectly?
Any explanation would be gretly appreciated.
Could you please provide some guidance on the following:
1) Sample Skewness and Kurtosis Formulas
I have seen 2 differnt versions,can you please clarify which is correct:
Version#1: Sample Skewness
Sum of Third moment about the mean / cube of Std Deviation * 1/ N...
I have a question regarding kurtosis and skewness.
In investment terms skewness is supposed to mean “bias toward positive or negative return”.
Kurtosis captures the tendency of the price of this investment to jump either direction. In FRM, I’ve encountered EVT, and its objective...