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Luis A. Afonso
Posts:
4,518
From:
LIsbon (Portugal)
Registered:
2/16/05


Just for fun
Posted:
Dec 30, 2013 3:01 PM


Just for fun
Noting that both U= (n/6)*S^2 and V= n/24*(K3)^2, JB=U(S) + V(k), do depend from the second central moment is intuitively obvious to assume that the two JarqueBera test statistics summands are strongly correlated. In order to try to destroy this feature we (just for fun) *split* the sample into two halves: firstly estimating the the third and the second then, the fourth and a fresh second moment. Note that in this instance we do not really split a sample, rather we *draw* (simulate) other sample.
Results:
We simulate the twosample way, n= 20 + 20 <APART> and the current way <JBcurrnt>, n= 40; the Quantiles Q from 0.05 to 0.95 are shown below.
___n=___20+20__40__________20+20__40__ ___Q__________________Q______________
__0.05___0.07__0.10____0.10___0.15__0.20_ __0.15___0.23__0.30____0.20___0.31__0.39_ __0.25___0.39__0.49____0.30___0.47__0.59_ __0.35___0.56__0.69____0.40___0.65__0.79_ __0.45___0.74__0.90____0.50___0.84__1.01_ __0.55___0.96__1.13____0.60___1.08__1.26_ __0.65___1.22__1.40____0.70___1.38__1.56_ __0.75___1.58__1.76____0.80___1.85__2.00_ __0.85___2.22__2.36____0.90___2.82__3.00_ __0.95___4.02__4.78____
Note that the values are quite similar, the present way only a little less disperse than the classic procedure, see:
arXiv:math/0509423v1 [math.ST] 19 Sep 2005
Luis A. Afonso



