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 $m$ > $p/2$.

Usage

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

Arguments

rData

a zoo/xts object containing all returns in period t for one asset.

the window size of return blocks. 2 by default.

the power of the variation. 2 by default.

alignBy

a string, align the tick data to "seconds"|"minutes"|"hours".

alignPeriod

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.

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.

Examples

Run this code

# NOT RUN {
data(sampleTData)
rMPV(sampleTData$PRICE, m = 2, p = 3, alignBy = "minutes", alignPeriod = 5, makeReturns = TRUE)

# }

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