変動性が変わる場合の利益率
最近ローゼンバーグ氏の論文を読みながら金融に関わる統計学を考えています。One nontrivial aspect of the paper was the use of lagging moving averages and two-sided moving averages. A second aspect was the division of the moving average by the standardized forecast standard deviation to determine whether fluctuations in variance are to blame for excess kurtosis.
The use of (gamma-3) instead of gamma as the multiple for the E(L(y^4)t )and E(L(mu4)t) is also puzzling.
Another mystery is the use of two separate Kurtosis formulas, kurtosis(v,y) and kurtosis(v,L,y). It seems the latter is the Kurtosis of a summation over L subintervals. The point seems to be that the kurtosis of a moving sum is less than the kurtosis of a variable itself, but the mathematics are unconvincing.
もう一つな不明点が発生しました。(gamma-3)*E*1/((Lvt)^2) +3 should equal gamma, it seems, as the numerator and denominator of the E term should cancel. However, the paper makes no such simplification.
The distinction of population moment vs. sample moment is also unclear, particularly whether "sample moment" corresponds to y or mu.
