rSV: Realized semivariance of highfrequency return series.
Description
Function returns Realized semivariance, defined in Barndorff-Nielsen et al. (2008).
Function returns two outcomes: 1.Downside realized semivariance and 2.Upside realized semivariance.
Assume there is $N$ equispaced returns in period $t$. Let $r_{t,i}$ be a return (with $i=1, \ldots,N$) in period $t$.
Then, the rSV is given by
$$\mbox{rSVdownside}_{t}= \sum_{i=1}^{N} (r_{t,i})^2 \ \times \ I [ r_{t,i} <0 ]$$="" $$\mbox{rsvupside}_{t}="\sum_{i=1}^{N}" (r_{t,i})^2="" \="" \times="" i="" [="" r_{t,i}="">0 ]$$