rMPVar: Realized multipower variation

Description

Calculate the Realized Multipower Variation rMPVar, defined in Andersen et al. (2012).

Assume there are $N$ equispaced returns $r_{t,i}$ in period $t$, $i=1, \ldots,N$. Then, the rMPVar is given by $$ \mbox{rMPVar}_{N}(m,p)= d_{m,p} \frac{N^{p/2}}{N-m+1} \sum_{i=1}^{N-m+1}|r_{t,i}|^{p/m} \ldots |r_{t,i+m-1}|^{p/m} $$

in which

$d_{m,p} = \mu_{p/m}^{-m}$:

$m$: the window size of return blocks;

$p$: the power of the variation;

and $m$ > $p/2$.

Usage

rMPVar(
  rData,
  m = 2,
  p = 2,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  ...
)

Value

numeric

Arguments

rData: an xts or data.table object containing returns or prices, possibly for multiple assets over multiple days.
m: the window size of return blocks. 2 by default.
p: the power of the variation. 2 by default.
alignBy: character, indicating the time scale in which alignPeriod is expressed. Possible values are: "ticks", "secs", "seconds", "mins", "minutes", "hours"
alignPeriod: positive numeric, indicating the number of periods to aggregate over. For example, to aggregate based on a 5-minute frequency, set alignPeriod = 5 and alignBy = "minutes".
makeReturns: boolean, should be TRUE when rData contains prices instead of returns. FALSE by default.
...: used internally, do not change.

Author

Giang Nguyen, Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

References

Andersen, T. G., Dobrev, D., and Schaumburg, E. (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169, 75-93.

Examples

Run this code

mpv <- rMPVar(sampleTData[, list(DT, PRICE)], m = 2, p = 3, alignBy = "minutes",
            alignPeriod = 5, makeReturns = TRUE)
mpv

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