rMPV: Realized multipower variation (MPV), an estimator of integrated power variation.
Description
Function returns the rMPV, defined in Andersen et al. (2012).
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 rMPV is given by
$$\mbox{rMPV}_{N}(m,p)= d_{m,p} \frac{N^{p/2}}{N-m+1} \sum_{i=1}^{N-m+1}|r_{t,i}|^{p/m} \ldots |r_{t,i+m-1}|^{p/m}$$
in which
$d_{m,p}= \mu_{p/m}^{-m}$:
$m$: the window size of return blocks;
$p$: the power of the variation;
and $m$ > $p/2$.
a zoo/xts object containing all returns in period t for one asset.
m
the window size of return blocks. 2 by default.
p
the power of the variation. 2 by default.
align.by
a string, align the tick data to "seconds"|"minutes"|"hours"
align.period
an integer, align the tick data to this many [seconds|minutes|hours].
makeReturns
boolean, should be TRUE when rdata contains prices instead of returns. FALSE by default.
...
additional arguments.
Value
numeric
References
Andersen, T. G., D. Dobrev, and E. Schaumburg (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169(1), 75- 93.